Pub Date : 2025-01-06DOI: 10.1016/j.jcp.2024.113715
Bingqian Si , Aaron Philip , Yuxiao Wei , Jianliang Qian
The original first-order accurate adjoint-state method for first-arrival traveltime tomography (Leung and Qian (2006) [12]) is based on first-order eikonal solvers and first-order adjoint-state solvers so that the resulting algorithm provides only low-resolution images. Therefore, to produce high-resolution images in first-arrival traveltime tomography, we propose a novel high-order accurate adjoint-state method which consists of three crucial ingredients: a high-order point-source eikonal solver to compute accurate traveltimes, a novel advection equation to uniformly back-propagate traveltime residuals, and a high-order adjoint-state solver to compute accurate adjoint states. 2-D and 3-D numerical results demonstrate that the new algorithm is able to produce high-resolution images in the setting of first-arrival transmission traveltime tomography.
{"title":"High-order accurate adjoint-state methods for three-dimensional high-resolution first-arrival traveltime tomography","authors":"Bingqian Si , Aaron Philip , Yuxiao Wei , Jianliang Qian","doi":"10.1016/j.jcp.2024.113715","DOIUrl":"10.1016/j.jcp.2024.113715","url":null,"abstract":"<div><div>The original first-order accurate adjoint-state method for first-arrival traveltime tomography (Leung and Qian (2006) <span><span>[12]</span></span>) is based on first-order eikonal solvers and first-order adjoint-state solvers so that the resulting algorithm provides only low-resolution images. Therefore, to produce high-resolution images in first-arrival traveltime tomography, we propose a novel high-order accurate adjoint-state method which consists of three crucial ingredients: a high-order point-source eikonal solver to compute accurate traveltimes, a novel advection equation to uniformly back-propagate traveltime residuals, and a high-order adjoint-state solver to compute accurate adjoint states. 2-D and 3-D numerical results demonstrate that the new algorithm is able to produce high-resolution images in the setting of first-arrival transmission traveltime tomography.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113715"},"PeriodicalIF":3.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.jcp.2024.113713
Kui Cao , Weixiong Yuan , Bin Zhang , Yiwei Feng , Tiegang Liu
It is well-known that convergence to steady state is hard when a high order discontinuous Galerkin (DG) method is applied for transonic and supersonic flows in polynomial space even with post-processing such as limiters and positivity preservation. The method discretizes the hyperbolic conservation laws in space in advance to obtain a system of first-order ordinary differential equations in time. As a result, steady-state solution of the DG method is equivalent to the equilibrium point of this system. In this paper, we analyze the stability of DG methods in the view point of dynamical systems for the scalar conservation law. We show that the steady-state solution of the 3rd-order DG method is not always stable in the presence of shock waves, and then we propose an artificial viscosity to stabilize the DG method and shows that the artificial viscosity has to be order one of the mesh size to improve stability. To maintain higher order accuracy, the proposed artificial viscosity is only applied in the vicinities of shock waves together with a shock-wave indicator. Numerical results are given to verify theoretical analysis. Several transonic/supersonic flow test cases are also present to demonstrate the effectiveness of the present artificial viscosity.
{"title":"Stabilized P2-DG method with artificial viscosity for steady hyperbolic conservation laws","authors":"Kui Cao , Weixiong Yuan , Bin Zhang , Yiwei Feng , Tiegang Liu","doi":"10.1016/j.jcp.2024.113713","DOIUrl":"10.1016/j.jcp.2024.113713","url":null,"abstract":"<div><div>It is well-known that convergence to steady state is hard when a high order discontinuous Galerkin (DG) method is applied for transonic and supersonic flows in polynomial space even with post-processing such as limiters and positivity preservation. The method discretizes the hyperbolic conservation laws in space in advance to obtain a system of first-order ordinary differential equations in time. As a result, steady-state solution of the DG method is equivalent to the equilibrium point of this system. In this paper, we analyze the stability of DG methods in the view point of dynamical systems for the scalar conservation law. We show that the steady-state solution of the 3rd-order DG method is not always stable in the presence of shock waves, and then we propose an artificial viscosity to stabilize the DG method and shows that the artificial viscosity has to be order one of the mesh size to improve stability. To maintain higher order accuracy, the proposed artificial viscosity is only applied in the vicinities of shock waves together with a shock-wave indicator. Numerical results are given to verify theoretical analysis. Several transonic/supersonic flow test cases are also present to demonstrate the effectiveness of the present artificial viscosity.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113713"},"PeriodicalIF":3.8,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113709
Nathan Gaby, Xiaojing Ye
We propose a finite-dimensional nonlinear model to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural network, we connect the evolution of the model parameters with trajectories in a corresponding function space. Using the computational technique of neural ordinary differential equation, we learn the control field over the parameter space such that from any initial starting point, the controlled trajectories closely approximate the solutions to the PDE. Approximation accuracy is justified for a general class of second-order nonlinear PDEs. Numerical results are presented for several high-dimensional PDEs, including real-world applications to solving Hamilton-Jacobi-Bellman equations. These are demonstrated to show the accuracy and efficiency of the proposed method.
{"title":"Approximation of solution operators for high-dimensional PDEs","authors":"Nathan Gaby, Xiaojing Ye","doi":"10.1016/j.jcp.2024.113709","DOIUrl":"10.1016/j.jcp.2024.113709","url":null,"abstract":"<div><div>We propose a finite-dimensional nonlinear model to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural network, we connect the evolution of the model parameters with trajectories in a corresponding function space. Using the computational technique of neural ordinary differential equation, we learn the control field over the parameter space such that from any initial starting point, the controlled trajectories closely approximate the solutions to the PDE. Approximation accuracy is justified for a general class of second-order nonlinear PDEs. Numerical results are presented for several high-dimensional PDEs, including real-world applications to solving Hamilton-Jacobi-Bellman equations. These are demonstrated to show the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113709"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113711
Wenxuan Xie , Zihan Wang , Junseok Kim , Xing Sun , Yibao Li
A novel ensemble Kalman filter based data assimilation method with an adaptive strategy is presented in this research work. The phase field dendritic crystal growth model is an effective tool to simulate the microstructural evolutions of dendritic crystal growth, while numerous simulation parameters must be determined to reproduce the experimentally observed microstructures. The ensemble Kalman filter (EnKF) method can be flexibly applied in phase field dendritic crystal growth simulation and achieve the inverse estimation of the simulation parameters, while it suffers from the issues of high computational cost and storage requirement. In this work, we integrate an adaptive strategy with the EnKF data assimilation. We define an adaptive narrow band domain as a neighboring region of the interface, which can accurately resolve the interfacial transition layer of the phase field. The local and low-dimensional observation data can be extracted from the narrow domain. By combining the adaptive strategy with the EnKF data assimilation, we reduce the high computational cost and storage requirement for the estimation of simulation parameters. We perform various twin experiments for both two- and three-dimensional phase field simulation of dendritic growth to assess the performance of our algorithm. The results reveal that the present method can achieve the desired estimation results using the low-dimensional observation data.
{"title":"A novel ensemble Kalman filter based data assimilation method with an adaptive strategy for dendritic crystal growth","authors":"Wenxuan Xie , Zihan Wang , Junseok Kim , Xing Sun , Yibao Li","doi":"10.1016/j.jcp.2024.113711","DOIUrl":"10.1016/j.jcp.2024.113711","url":null,"abstract":"<div><div>A novel ensemble Kalman filter based data assimilation method with an adaptive strategy is presented in this research work. The phase field dendritic crystal growth model is an effective tool to simulate the microstructural evolutions of dendritic crystal growth, while numerous simulation parameters must be determined to reproduce the experimentally observed microstructures. The ensemble Kalman filter (EnKF) method can be flexibly applied in phase field dendritic crystal growth simulation and achieve the inverse estimation of the simulation parameters, while it suffers from the issues of high computational cost and storage requirement. In this work, we integrate an adaptive strategy with the EnKF data assimilation. We define an adaptive narrow band domain as a neighboring region of the interface, which can accurately resolve the interfacial transition layer of the phase field. The local and low-dimensional observation data can be extracted from the narrow domain. By combining the adaptive strategy with the EnKF data assimilation, we reduce the high computational cost and storage requirement for the estimation of simulation parameters. We perform various twin experiments for both two- and three-dimensional phase field simulation of dendritic growth to assess the performance of our algorithm. The results reveal that the present method can achieve the desired estimation results using the low-dimensional observation data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113711"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113708
Gabriele Immordino , Andrea Vaiuso , Andrea Da Ronch , Marcello Righi
This paper addresses the challenges posed by non-homogeneous unstructured grids, which are commonly used in computational fluid dynamics. The prevalence of these grids in fluid dynamics scenarios has driven the exploration of innovative approaches for generating reduced-order models. Our approach leverages geometric deep learning, specifically through the use of an autoencoder architecture built on graph convolutional networks. This architecture enhances prediction accuracy by propagating information to distant nodes and emphasizing influential points. Key innovations include a dimensionality reduction module based on pressure-gradient values, fast connectivity reconstruction using Mahalanobis distance, optimization of the network architecture, and a physics-informed loss function based on aerodynamic coefficient. These advancements result in a more robust and accurate predictive model, achieving systematically lower errors compared to previous graph-based methods. The proposed methodology is validated through two distinct test cases—wing-only and wing-body configurations—demonstrating precise reconstruction of steady-state distributed quantities within a two-dimensional parametric space.
{"title":"Predicting transonic flowfields in non–homogeneous unstructured grids using autoencoder graph convolutional networks","authors":"Gabriele Immordino , Andrea Vaiuso , Andrea Da Ronch , Marcello Righi","doi":"10.1016/j.jcp.2024.113708","DOIUrl":"10.1016/j.jcp.2024.113708","url":null,"abstract":"<div><div>This paper addresses the challenges posed by non-homogeneous unstructured grids, which are commonly used in computational fluid dynamics. The prevalence of these grids in fluid dynamics scenarios has driven the exploration of innovative approaches for generating reduced-order models. Our approach leverages geometric deep learning, specifically through the use of an autoencoder architecture built on graph convolutional networks. This architecture enhances prediction accuracy by propagating information to distant nodes and emphasizing influential points. Key innovations include a dimensionality reduction module based on pressure-gradient values, fast connectivity reconstruction using Mahalanobis distance, optimization of the network architecture, and a physics-informed loss function based on aerodynamic coefficient. These advancements result in a more robust and accurate predictive model, achieving systematically lower errors compared to previous graph-based methods. The proposed methodology is validated through two distinct test cases—wing-only and wing-body configurations—demonstrating precise reconstruction of steady-state distributed quantities within a two-dimensional parametric space.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113708"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113710
Xuehan Zhang, Lijian Jiang
In this paper, we combine convolutional neural networks (CNNs) with reduced order modeling (ROM) for efficient simulations of multiscale problems. These problems are modeled by partial differential equations with high-dimensional random inputs. The proposed method involves two separate CNNs: Basis CNNs and Coefficient CNNs (Coef CNNs), which correspond to two main parts of ROM. The method is thus called CNN-based ROM. The former one learns input-specific basis functions from the snapshots of fine-scale solutions. An activation function, inspired by Galerkin projection, is utilized at the output layer to reconstruct fine-scale solutions from the basis functions. Numerical results show that the basis functions learned by the Basis CNNs resemble data, which help to significantly reduce the number of the basis functions. Moreover, CNN-based ROM is less sensitive to data fluctuation caused by numerical errors than traditional ROM. Since the tests of Basis CNNs still need fine-scale stiffness matrix and load vector, it can not be directly applied to nonlinear problems. The latter CNNs, called Coef CNNs, are then designed to determine the coefficients for linear combination of basis functions. In addition, two applications of CNN-based ROM are presented, including predicting MsFEM basis functions within large oversampling regions and building accurate surrogates for inverse problems.
{"title":"Convolutional neural network based reduced order modeling for multiscale problems","authors":"Xuehan Zhang, Lijian Jiang","doi":"10.1016/j.jcp.2024.113710","DOIUrl":"10.1016/j.jcp.2024.113710","url":null,"abstract":"<div><div>In this paper, we combine convolutional neural networks (CNNs) with reduced order modeling (ROM) for efficient simulations of multiscale problems. These problems are modeled by partial differential equations with high-dimensional random inputs. The proposed method involves two separate CNNs: Basis CNNs and Coefficient CNNs (Coef CNNs), which correspond to two main parts of ROM. The method is thus called CNN-based ROM. The former one learns input-specific basis functions from the snapshots of fine-scale solutions. An activation function, inspired by Galerkin projection, is utilized at the output layer to reconstruct fine-scale solutions from the basis functions. Numerical results show that the basis functions learned by the Basis CNNs resemble data, which help to significantly reduce the number of the basis functions. Moreover, CNN-based ROM is less sensitive to data fluctuation caused by numerical errors than traditional ROM. Since the tests of Basis CNNs still need fine-scale stiffness matrix and load vector, it can not be directly applied to nonlinear problems. The latter CNNs, called Coef CNNs, are then designed to determine the coefficients for linear combination of basis functions. In addition, two applications of CNN-based ROM are presented, including predicting MsFEM basis functions within large oversampling regions and building accurate surrogates for inverse problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113710"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113712
N. Anders Petersson, Stefanie Günther, Seung Whan Chung
Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. This enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.
{"title":"A time-parallel multiple-shooting method for large-scale quantum optimal control","authors":"N. Anders Petersson, Stefanie Günther, Seung Whan Chung","doi":"10.1016/j.jcp.2024.113712","DOIUrl":"10.1016/j.jcp.2024.113712","url":null,"abstract":"<div><div>Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. This enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113712"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.jcp.2024.113705
Zijie Li , Saurabh Patil , Francis Ogoke , Dule Shu , Wilson Zhen , Michael Schneier , John R. Buchanan Jr. , Amir Barati Farimani
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional discretized fields, we propose to learn the dynamics of the system in the latent space with much coarser discretizations. In our proposed framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space, then a temporal model is trained to predict the future state in this mesh-reduced space. This reduction process simplifies the training of the temporal model by greatly reducing the computational cost accompanying a fine discretization and enables more efficient backprop-through-time training. We study the capability of the proposed framework and several other popular neural PDE solvers on various types of systems including single-phase and multi-phase flows along with varying system parameters. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.
{"title":"Latent neural PDE solver: A reduced-order modeling framework for partial differential equations","authors":"Zijie Li , Saurabh Patil , Francis Ogoke , Dule Shu , Wilson Zhen , Michael Schneier , John R. Buchanan Jr. , Amir Barati Farimani","doi":"10.1016/j.jcp.2024.113705","DOIUrl":"10.1016/j.jcp.2024.113705","url":null,"abstract":"<div><div>Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional discretized fields, we propose to learn the dynamics of the system in the latent space with much coarser discretizations. In our proposed framework - Latent Neural PDE Solver (LNS), a non-linear autoencoder is first trained to project the full-order representation of the system onto the mesh-reduced space, then a temporal model is trained to predict the future state in this mesh-reduced space. This reduction process simplifies the training of the temporal model by greatly reducing the computational cost accompanying a fine discretization and enables more efficient backprop-through-time training. We study the capability of the proposed framework and several other popular neural PDE solvers on various types of systems including single-phase and multi-phase flows along with varying system parameters. We showcase that it has competitive accuracy and efficiency compared to the neural PDE solver that operates on full-order space.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113705"},"PeriodicalIF":3.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-31DOI: 10.1016/j.jcp.2024.113702
Wenbin Zhang , Thomas Paula , Alexander Bußmann , Stefan Adami , Nikolaus A. Adams
We extend the hybrid reconstruction method combining the fifth-order incremental-stencil weighted essential non-oscillatory (WENO5IS) with the Tangent of Hyperbola for INterface Capturing (THINC) to flow scenarios involving an arbitrary number of fluids. The extended five-equation model accounting for both capillary and viscous forces is employed, maintaining permutation symmetry among fluid components. Within the finite volume (FV) framework employing structured meshes, the WENO5IS scheme, augmented with a positivity-preserving limiter accurately resolves flow structures inside each component, while the symmetry-preserving THINC sharpens the fluid interfaces. Interface regions containing multiple components are decomposed into pairs of interfaces between each involved component, and the corresponding reconstructed volume fractions and phase densities are renormalized before time integration. The inclusion of a generalized continuous surface force (CSF) method enables simulation of capillary effects between an arbitrary number of fluids. One- and two-dimensional test cases involving multiple components are employed to validate the efficacy of the proposed approach in maintaining interface sharpness, achieving high-resolution within individual components, and preserving normalization and positivity properties of volume fractions. Simulations incorporating surface tension and viscosity further demonstrate the applicability of the present model and algorithm in capillary problems within the compressible framework.
{"title":"Extension of the hybrid WENO5IS-THINC scheme to compressible multiphase flows with an arbitrary number of components","authors":"Wenbin Zhang , Thomas Paula , Alexander Bußmann , Stefan Adami , Nikolaus A. Adams","doi":"10.1016/j.jcp.2024.113702","DOIUrl":"10.1016/j.jcp.2024.113702","url":null,"abstract":"<div><div>We extend the hybrid reconstruction method combining the fifth-order incremental-stencil weighted essential non-oscillatory (WENO5IS) with the Tangent of Hyperbola for INterface Capturing (THINC) to flow scenarios involving an arbitrary number of fluids. The extended five-equation model accounting for both capillary and viscous forces is employed, maintaining permutation symmetry among fluid components. Within the finite volume (FV) framework employing structured meshes, the WENO5IS scheme, augmented with a positivity-preserving limiter accurately resolves flow structures inside each component, while the symmetry-preserving THINC sharpens the fluid interfaces. Interface regions containing multiple components are decomposed into pairs of interfaces between each involved component, and the corresponding reconstructed volume fractions and phase densities are renormalized before time integration. The inclusion of a generalized continuous surface force (CSF) method enables simulation of capillary effects between an arbitrary number of fluids. One- and two-dimensional test cases involving multiple components are employed to validate the efficacy of the proposed approach in maintaining interface sharpness, achieving high-resolution within individual components, and preserving normalization and positivity properties of volume fractions. Simulations incorporating surface tension and viscosity further demonstrate the applicability of the present model and algorithm in capillary problems within the compressible framework.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113702"},"PeriodicalIF":3.8,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-31DOI: 10.1016/j.jcp.2024.113704
Jordi Poblador-Ibanez, Nicolás Valle, Bendiks Jan Boersma
A proven methodology to solve multiphase flows is based on the one-fluid formulation of the governing equations, which treats the phase transition across the interface as a single fluid with varying properties and adds additional source terms to satisfy interface jump conditions, e.g., surface tension and mass transfer. Used interchangeably in the limit of non-evaporative flows, recent literature has formalized the inconsistencies that arise in the momentum balance of the non-conservative one-fluid formulation compared to its conservative counterpart when phase change is involved. This translates into an increased sensitivity of the numerical solution to the choice of formulation. Motivated by the fact that many legacy codes using the non-conservative one-fluid formulation have been extended to phase-change simulations, the inclusion of two corrective forces at the interface and a modification of the pressure-velocity solver with an additional predictor-projection step are shown to recover the exact momentum balance in the evaporative non-conservative one-fluid framework for low-viscosity incompressible flows. This has direct implications for obtaining a physically meaningful pressure jump across the interface and is seen to affect the dynamics of two-phase flows. In the high-viscosity domain, the discretization of the viscous term introduces a momentum imbalance which is highly dependent on the chosen method to model the phase transition. In the context of film boiling, this imbalance affects the time scales for the instability growth. Lastly, the need to develop sub-models for heat and mass transfer and for surface tension becomes evident since typical grid resolutions defined as “resolved” in the literature may not be enough to capture interfacial phenomena.
{"title":"A momentum balance correction to the non-conservative one-fluid formulation in boiling flows using volume-of-fluid","authors":"Jordi Poblador-Ibanez, Nicolás Valle, Bendiks Jan Boersma","doi":"10.1016/j.jcp.2024.113704","DOIUrl":"10.1016/j.jcp.2024.113704","url":null,"abstract":"<div><div>A proven methodology to solve multiphase flows is based on the one-fluid formulation of the governing equations, which treats the phase transition across the interface as a single fluid with varying properties and adds additional source terms to satisfy interface jump conditions, e.g., surface tension and mass transfer. Used interchangeably in the limit of non-evaporative flows, recent literature has formalized the inconsistencies that arise in the momentum balance of the non-conservative one-fluid formulation compared to its conservative counterpart when phase change is involved. This translates into an increased sensitivity of the numerical solution to the choice of formulation. Motivated by the fact that many legacy codes using the non-conservative one-fluid formulation have been extended to phase-change simulations, the inclusion of two corrective forces at the interface and a modification of the pressure-velocity solver with an additional predictor-projection step are shown to recover the exact momentum balance in the evaporative non-conservative one-fluid framework for low-viscosity incompressible flows. This has direct implications for obtaining a physically meaningful pressure jump across the interface and is seen to affect the dynamics of two-phase flows. In the high-viscosity domain, the discretization of the viscous term introduces a momentum imbalance which is highly dependent on the chosen method to model the phase transition. In the context of film boiling, this imbalance affects the time scales for the instability growth. Lastly, the need to develop sub-models for heat and mass transfer and for surface tension becomes evident since typical grid resolutions defined as “resolved” in the literature may not be enough to capture interfacial phenomena.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113704"},"PeriodicalIF":3.8,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号