Pub Date : 2024-11-22DOI: 10.1016/j.jcp.2024.113604
Alexander A. Belozerov, Natalia B. Petrovskaya, Yulii D. Shikhmurzaev
The Darcy model for flows in porous media is hugely popular among researchers and practitioners yet there are many problems where the classical Darcy model is not efficient and accurate as it gives rise to manifestly nonphysical singularities. We aim to investigate numerically a new class of mathematical models that allow for handling nonphysical singularities while preserving the advantages of the classical Darcy model. The introduced dependence of the permeability of the porous matrix on the flow that passes through it makes it necessary to compute the flow field and the permeability field simultaneously, and we therefore develop a novel numerical method to compute the solution to a strongly nonlinear system of PDEs arising in the problem. Our approach allows one to take characteristics of the flow geometry into account in numerical solution and we demonstrate the predictive potential of the generalized Darcy model through numerical tests.
{"title":"Numerical investigation of a new class of models of Darcy-scale flows with flow-dependent permeability","authors":"Alexander A. Belozerov, Natalia B. Petrovskaya, Yulii D. Shikhmurzaev","doi":"10.1016/j.jcp.2024.113604","DOIUrl":"10.1016/j.jcp.2024.113604","url":null,"abstract":"<div><div>The Darcy model for flows in porous media is hugely popular among researchers and practitioners yet there are many problems where the classical Darcy model is not efficient and accurate as it gives rise to manifestly nonphysical singularities. We aim to investigate numerically a new class of mathematical models that allow for handling nonphysical singularities while preserving the advantages of the classical Darcy model. The introduced dependence of the permeability of the porous matrix on the flow that passes through it makes it necessary to compute the flow field and the permeability field simultaneously, and we therefore develop a novel numerical method to compute the solution to a strongly nonlinear system of PDEs arising in the problem. Our approach allows one to take characteristics of the flow geometry into account in numerical solution and we demonstrate the predictive potential of the generalized Darcy model through numerical tests.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113604"},"PeriodicalIF":3.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723648","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 : 2024-11-22DOI: 10.1016/j.jcp.2024.113603
Changqing Ye , Shubin Fu , Eric T. Chung , Jizu Huang
In this paper, we develop a highly parallelized preconditioner based on multiscale space to tackle Darcy flow in highly heterogeneous porous media. The crucial component of this preconditioner is devising a sequence of nested subspaces: . By defining an appropriate spectral problem within the space of , we leverage the eigenfunctions of these spectral problems to form . The preconditioner is then employed to solve a positive semidefinite linear system, which arises from discretizing the Darcy flow equation using the lowest order Raviart-Thomas spaces and adopting a trapezoidal quadrature rule. We will present both theoretical analysis and numerical investigations of this preconditioner. In particular, we will explore various highly heterogeneous permeability fields with resolutions of up to 10243, evaluating the computational performance of the preconditioner in several aspects, including strong scalability, weak scalability, and robustness against the contrast ratio of the media. In high-contrast settings, the proposed preconditioner demonstrates superior performance in terms of stability and efficiency compared to the default algebraic multigrid solver in PETSc, a renowned high performance computing library. A numerical experiment will showcase the preconditioner's capability to solve a high-contrast, large-scale problem with 10243 degrees of freedom using just 1728 CPU cores with 30 seconds. Furthermore, we will demonstrate the application of this preconditioner in solving benchmark problems related to two-phase flow.
{"title":"A highly parallelized multiscale preconditioner for Darcy flow in high-contrast media","authors":"Changqing Ye , Shubin Fu , Eric T. Chung , Jizu Huang","doi":"10.1016/j.jcp.2024.113603","DOIUrl":"10.1016/j.jcp.2024.113603","url":null,"abstract":"<div><div>In this paper, we develop a highly parallelized preconditioner based on multiscale space to tackle Darcy flow in highly heterogeneous porous media. The crucial component of this preconditioner is devising a sequence of nested subspaces: <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>L</mi></mrow></msub><mo>⊂</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>L</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⊂</mo><mo>…</mo><mo>⊂</mo><msub><mrow><mi>W</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>. By defining an appropriate spectral problem within the space of <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub></math></span>, we leverage the eigenfunctions of these spectral problems to form <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. The preconditioner is then employed to solve a positive semidefinite linear system, which arises from discretizing the Darcy flow equation using the lowest order Raviart-Thomas spaces and adopting a trapezoidal quadrature rule. We will present both theoretical analysis and numerical investigations of this preconditioner. In particular, we will explore various highly heterogeneous permeability fields with resolutions of up to 1024<sup>3</sup>, evaluating the computational performance of the preconditioner in several aspects, including strong scalability, weak scalability, and robustness against the contrast ratio of the media. In high-contrast settings, the proposed preconditioner demonstrates superior performance in terms of stability and efficiency compared to the default algebraic multigrid solver in PETSc, a renowned high performance computing library. A numerical experiment will showcase the preconditioner's capability to solve a high-contrast, large-scale problem with 1024<sup>3</sup> degrees of freedom using just 1728 CPU cores with 30 seconds. Furthermore, we will demonstrate the application of this preconditioner in solving benchmark problems related to two-phase flow.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113603"},"PeriodicalIF":3.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723595","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 : 2024-11-22DOI: 10.1016/j.jcp.2024.113600
Arijit Sinhababu, Shyamprasad Karagadde
In the present study, a Fourier pseudo-spectral-based, phase-field framework is developed to simulate the binary alloy solidification using fixed grids. The motivation behind this proposition of a new model towards overcoming existing limitations is two-fold: firstly, to create a fully validated high-order phase-field model that closely aligns with LKT predictions of tip kinetics across various undercoolings and compositions, and secondly, to achieve accurate simulations using fixed Cartesian meshes with a grid size of order more than unity. In the Fourier pseudo-spectral method, the nonlinear terms of the PF equations are de-aliased using zero padding and high-order Fourier smoothing exponential filters. Accurate growth kinetics during binary alloy solidification are observed despite employing fixed mesh sizes, even when the ratio of grid size to diffuse interface thickness is 1.42. A hybrid, integrating factor (IF)-based, strongly stable third-order Runge-Kutta method (SSPRK3) is implemented to obtain improved temporal stability at high Lewis numbers. A novel scaling relationship between dimensionless tip velocity and undercooling is obtained from the growth of a four-arm equiaxed dendrite at different levels of undercooling. The growth of several randomly oriented dendrites is also accurately simulated without using any mesh refinement schemes. Likewise, the tip velocity closely matched the LKT predictions at dilute concentrations at the boundary. Furthermore, the effects of the coupling parameter and the anti-trapping term on dendritic growth kinetics are explored. Overall, the proposed FFT-based framework is expected to capture the crystals' global chemical wave features precisely with fewer points per wavelength (PPW) and has the potential to be scaled up for large-scale simulations.
{"title":"A FFT-based phase-field framework for simulating dendritic growth in binary alloy","authors":"Arijit Sinhababu, Shyamprasad Karagadde","doi":"10.1016/j.jcp.2024.113600","DOIUrl":"10.1016/j.jcp.2024.113600","url":null,"abstract":"<div><div>In the present study, a Fourier pseudo-spectral-based, phase-field framework is developed to simulate the binary alloy solidification using fixed grids. The motivation behind this proposition of a new model towards overcoming existing limitations is two-fold: firstly, to create a fully validated high-order phase-field model that closely aligns with LKT predictions of tip kinetics across various undercoolings and compositions, and secondly, to achieve accurate simulations using fixed Cartesian meshes with a grid size of order more than unity. In the Fourier pseudo-spectral method, the nonlinear terms of the PF equations are de-aliased using zero padding and high-order Fourier smoothing exponential filters. Accurate growth kinetics during binary alloy solidification are observed despite employing fixed mesh sizes, even when the ratio of grid size to diffuse interface thickness is 1.42. A hybrid, integrating factor (IF)-based, strongly stable third-order Runge-Kutta method (SSPRK3) is implemented to obtain improved temporal stability at high Lewis numbers. A novel scaling relationship between dimensionless tip velocity and undercooling is obtained from the growth of a four-arm equiaxed dendrite at different levels of undercooling. The growth of several randomly oriented dendrites is also accurately simulated without using any mesh refinement schemes. Likewise, the tip velocity closely matched the LKT predictions at dilute concentrations at the boundary. Furthermore, the effects of the coupling parameter and the anti-trapping term on dendritic growth kinetics are explored. Overall, the proposed FFT-based framework is expected to capture the crystals' global chemical wave features precisely with fewer points per wavelength (PPW) and has the potential to be scaled up for large-scale simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113600"},"PeriodicalIF":3.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723647","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 : 2024-11-21DOI: 10.1016/j.jcp.2024.113621
Ke Xu , Zhenxun Gao , Zhansen Qian , Chongwen Jiang , Chun-Hian Lee
Pseudo-convergence appears when ideal magnetohydrodynamic (MHD) equations are numerically solved, i.e., a converged numerical solution cannot be obtained even by continuously refining the grids under the initial condition of a large angle of the tangential magnetic field. However, the current numerical methods for pseudo-convergence have not explored the intrinsic cause of pseudo-convergence. Therefore, the current numerical schemes cannot completely eliminate the pseudo-convergence phenomenon. In this paper, we first perform an in-depth analysis of pseudo-convergence and find that the essence of pseudo-convergence lies in the unphysical averaging process of the existing numerical schemes for the Alfvénic waves. Based on this finding, the merits of numerical path preserving (NPP) of the Godunov scheme are generalized to correct the eigenvalues, eigenvectors, and wave strength of the Alfvénic field in the MHD Roe scheme, and the novel NPP-Roe scheme is constructed so that the Alfvénic field can be captured correctly. Compared with the traditional Roe scheme, numerical validation shows that NPP-Roe scheme significantly reduces the computational grid requirements for the numerical simulation of the MHD problem and eliminates the pseudo-convergence phenomenon of the MHD problem by directly reducing the absolute error magnitude. In addition, for Riemann problems with tangential symmetry (e.g., 180° Alfvénic wave, Brio & Wu problem), the NPP-Roe scheme is also able to simulate the exact regular solutions that cannot be obtained by the traditional Roe scheme, which indicates that the NPP-Roe scheme expands the application range of the traditional scheme.
{"title":"Numerical path preserving Roe scheme for ideal MHD Riemann problem: Complete elimination of pseudo-convergence","authors":"Ke Xu , Zhenxun Gao , Zhansen Qian , Chongwen Jiang , Chun-Hian Lee","doi":"10.1016/j.jcp.2024.113621","DOIUrl":"10.1016/j.jcp.2024.113621","url":null,"abstract":"<div><div>Pseudo-convergence appears when ideal magnetohydrodynamic (MHD) equations are numerically solved, i.e., a converged numerical solution cannot be obtained even by continuously refining the grids under the initial condition of a large angle of the tangential magnetic field. However, the current numerical methods for pseudo-convergence have not explored the intrinsic cause of pseudo-convergence. Therefore, the current numerical schemes cannot completely eliminate the pseudo-convergence phenomenon. In this paper, we first perform an in-depth analysis of pseudo-convergence and find that the essence of pseudo-convergence lies in the unphysical averaging process of the existing numerical schemes for the Alfvénic waves. Based on this finding, the merits of numerical path preserving (NPP) of the Godunov scheme are generalized to correct the eigenvalues, eigenvectors, and wave strength of the Alfvénic field in the MHD Roe scheme, and the novel NPP-Roe scheme is constructed so that the Alfvénic field can be captured correctly. Compared with the traditional Roe scheme, numerical validation shows that NPP-Roe scheme significantly reduces the computational grid requirements for the numerical simulation of the MHD problem and eliminates the pseudo-convergence phenomenon of the MHD problem by directly reducing the absolute error magnitude. In addition, for Riemann problems with tangential symmetry (e.g., 180° Alfvénic wave, Brio & Wu problem), the NPP-Roe scheme is also able to simulate the exact regular solutions that cannot be obtained by the traditional Roe scheme, which indicates that the NPP-Roe scheme expands the application range of the traditional scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"523 ","pages":"Article 113621"},"PeriodicalIF":3.8,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747018","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 : 2024-11-21DOI: 10.1016/j.jcp.2024.113597
Allen Alvarez Loya , Daniel Appelö , William D. Henshaw
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time (FOT) and second-order-in-time (SOT) Hermite schemes are developed. Hermite methods use the solution and multiple derivatives as unknowns and achieve space-time orders of accuracy (FOT) and 2m (SOT) for methods using degree of freedom per node in d dimensions. The compatibility boundary conditions (CBCs) are based on taking time derivatives of the boundary conditions and using the governing equations to replace the time derivatives with spatial derivatives. These resulting constraint equations augment the Hermite scheme on the boundary. The solvability of the equations resulting from the compatibility conditions is analyzed. Numerical examples demonstrate the accuracy and stability of the new schemes in two dimensions.
{"title":"High order accurate Hermite schemes on curvilinear grids with compatibility boundary conditions","authors":"Allen Alvarez Loya , Daniel Appelö , William D. Henshaw","doi":"10.1016/j.jcp.2024.113597","DOIUrl":"10.1016/j.jcp.2024.113597","url":null,"abstract":"<div><div>High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time (FOT) and second-order-in-time (SOT) Hermite schemes are developed. Hermite methods use the solution and multiple derivatives as unknowns and achieve space-time orders of accuracy <span><math><mn>2</mn><mi>m</mi><mo>−</mo><mn>1</mn></math></span> (FOT) and 2<em>m</em> (SOT) for methods using <span><math><msup><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>d</mi></mrow></msup></math></span> degree of freedom per node in <em>d</em> dimensions. The compatibility boundary conditions (CBCs) are based on taking time derivatives of the boundary conditions and using the governing equations to replace the time derivatives with spatial derivatives. These resulting constraint equations augment the Hermite scheme on the boundary. The solvability of the equations resulting from the compatibility conditions is analyzed. Numerical examples demonstrate the accuracy and stability of the new schemes in two dimensions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113597"},"PeriodicalIF":3.8,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723642","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 : 2024-11-20DOI: 10.1016/j.jcp.2024.113598
Qi Hong , Zengyan Zhang , Jia Zhao
In this paper, we introduce a novel approach for formulating phase field models with constraints. The main idea is to introduce auxiliary variables that regularize and gradually dissipate constraint deviations of the phase variables, which we name the auxiliary relaxation method. It integrates seamlessly with the energy variational framework to ensure thermodynamic consistency in the resulting phase field models. Unlike traditional penalty methods, which introduce high stiffness due to large penalty parameters to enforce constraints in phase field models, our approach reduces system stiffness, allowing larger time step sizes when solving phase field models with constraints numerically, thus improving numerical accuracy and efficiency. We demonstrate the effectiveness and robustness of the proposed auxiliary relaxation method by applying it across several scenarios to derive thermodynamically consistent phase field models with constraints. Furthermore, we introduce a general second-order implicit-explicit Crank-Nicolson scheme, combining the relaxed scalar auxiliary variable method with a stabilization technique to solve these models. Through extensive numerical tests, we validate the capability of our modeling and numerical framework to reliably simulate complex dynamics governed by phase field equations with constraints.
{"title":"Auxiliary relaxation method to derive thermodynamically consistent phase field models with constraints and structure preserving numerical approximations","authors":"Qi Hong , Zengyan Zhang , Jia Zhao","doi":"10.1016/j.jcp.2024.113598","DOIUrl":"10.1016/j.jcp.2024.113598","url":null,"abstract":"<div><div>In this paper, we introduce a novel approach for formulating phase field models with constraints. The main idea is to introduce auxiliary variables that regularize and gradually dissipate constraint deviations of the phase variables, which we name the auxiliary relaxation method. It integrates seamlessly with the energy variational framework to ensure thermodynamic consistency in the resulting phase field models. Unlike traditional penalty methods, which introduce high stiffness due to large penalty parameters to enforce constraints in phase field models, our approach reduces system stiffness, allowing larger time step sizes when solving phase field models with constraints numerically, thus improving numerical accuracy and efficiency. We demonstrate the effectiveness and robustness of the proposed auxiliary relaxation method by applying it across several scenarios to derive thermodynamically consistent phase field models with constraints. Furthermore, we introduce a general second-order implicit-explicit Crank-Nicolson scheme, combining the relaxed scalar auxiliary variable method with a stabilization technique to solve these models. Through extensive numerical tests, we validate the capability of our modeling and numerical framework to reliably simulate complex dynamics governed by phase field equations with constraints.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113598"},"PeriodicalIF":3.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743160","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 : 2024-11-20DOI: 10.1016/j.jcp.2024.113599
A. Gogoi , J.C. Mandal , A. Saraf
The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities is found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.
{"title":"Stability evaluation of approximate Riemann solvers using the direct Lyapunov method","authors":"A. Gogoi , J.C. Mandal , A. Saraf","doi":"10.1016/j.jcp.2024.113599","DOIUrl":"10.1016/j.jcp.2024.113599","url":null,"abstract":"<div><div>The paper presents a new approach of stability evaluation of the approximate Riemann solvers based on the direct Lyapunov method. The present methodology offers a detailed understanding of the origins of numerical shock instability in approximate Riemann solvers. The pressure perturbation feeding the density and transverse momentum perturbations is identified as the cause of the numerical shock instabilities in the complete approximate Riemann solvers, while the magnitude of the numerical shock instabilities is found to be proportional to the magnitude of the pressure perturbations. A shock-stable HLLEM scheme is proposed based on the insights obtained from this analysis about the origins of numerical shock instability in the approximate Riemann solvers. A set of numerical test cases are solved to show that the proposed scheme is free from numerical shock instability problems of the original HLLEM scheme at high Mach numbers.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113599"},"PeriodicalIF":3.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706988","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 : 2024-11-20DOI: 10.1016/j.jcp.2024.113601
Jianguo Huang , Yue Qiu
Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO has demonstrated the superiority of solving partial differential equations (PDEs) over other deep learning methods. However, for the widely used Fourier neural operator (FNO), the spatial domain of its input function needs to be identical to its output, i.e., FNO fails to approximate the map from boundary conditions to PDE solutions, which limits its applicability. To address this issue, we propose a novel framework called resolution-invariant deep operator (RDO) that decouples the spatial domain of the input and output. RDO is motivated by the Deep operator network (DeepONet) and it does not require retraining the network when the input/output is changed compared with DeepONet. RDO takes functional input and its output is also functional so that it keeps the resolution invariant property of NO. It can also resolve PDEs with complex geometries whereas FNO fails. Various numerical experiments demonstrate the advantage of our method over DeepONet and FNO.
{"title":"Resolution invariant deep operator network for PDEs with complex geometries","authors":"Jianguo Huang , Yue Qiu","doi":"10.1016/j.jcp.2024.113601","DOIUrl":"10.1016/j.jcp.2024.113601","url":null,"abstract":"<div><div>Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO has demonstrated the superiority of solving partial differential equations (PDEs) over other deep learning methods. However, for the widely used Fourier neural operator (FNO), the spatial domain of its input function needs to be identical to its output, i.e., FNO fails to approximate the map from boundary conditions to PDE solutions, which limits its applicability. To address this issue, we propose a novel framework called resolution-invariant deep operator (RDO) that decouples the spatial domain of the input and output. RDO is motivated by the Deep operator network (DeepONet) and it does not require retraining the network when the input/output is changed compared with DeepONet. RDO takes functional input and its output is also functional so that it keeps the resolution invariant property of NO. It can also resolve PDEs with complex geometries whereas FNO fails. Various numerical experiments demonstrate the advantage of our method over DeepONet and FNO.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113601"},"PeriodicalIF":3.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706984","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 : 2024-11-20DOI: 10.1016/j.jcp.2024.113602
Yu Fan , Shuoguo Zhang , Xiaoliang Li , Yujie Zhu , Xiangyu Hu , Nikolaus A. Adams
In this paper, we develop a hybrid method for insoluble surfactant dynamics. While the Navier-Stokes equations are solved by an Eulerian method with level set describing the interfaces, the surfactant transport is tracked by a single-layer Lagrangian particle method. Consequently, this hybrid method inherits the ability in handling topology changes from the level-set method and high computational efficiency from the Eulerian method. On the other hand, the Lagrangian particle method ensures mass conservation and does not require topology information (connectivity). To prevent clustering of Lagrangian particles, a novel remeshing approach is proposed. It not only enables the generation of particle distributions adaptive to interface geometries, especially for extremely large deformation and strong stretching, but also provides an accurate reconstruction of concentration fields on the interface with mass conservation. Furthermore, by proposing an adaptive remeshing control, we optimize the remeshing frequency to balance computational costs and accuracy. Conservation, accuracy, and convergence of the present hybrid method are validated with 2-D and 3-D test cases.
{"title":"A hybrid method for insoluble surfactant dynamics","authors":"Yu Fan , Shuoguo Zhang , Xiaoliang Li , Yujie Zhu , Xiangyu Hu , Nikolaus A. Adams","doi":"10.1016/j.jcp.2024.113602","DOIUrl":"10.1016/j.jcp.2024.113602","url":null,"abstract":"<div><div>In this paper, we develop a hybrid method for insoluble surfactant dynamics. While the Navier-Stokes equations are solved by an Eulerian method with level set describing the interfaces, the surfactant transport is tracked by a single-layer Lagrangian particle method. Consequently, this hybrid method inherits the ability in handling topology changes from the level-set method and high computational efficiency from the Eulerian method. On the other hand, the Lagrangian particle method ensures mass conservation and does not require topology information (connectivity). To prevent clustering of Lagrangian particles, a novel remeshing approach is proposed. It not only enables the generation of particle distributions adaptive to interface geometries, especially for extremely large deformation and strong stretching, but also provides an accurate reconstruction of concentration fields on the interface with mass conservation. Furthermore, by proposing an adaptive remeshing control, we optimize the remeshing frequency to balance computational costs and accuracy. Conservation, accuracy, and convergence of the present hybrid method are validated with 2-D and 3-D test cases.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113602"},"PeriodicalIF":3.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142743162","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}
We have developed a new computational method called the rotating flux-tube model that treats background shear flows in local gyrokinetic simulations. The method is based on extended magnetohydrodynamic ballooning mode theory. A coordinate transformation moves the flux-tube simulation domain along the sheared magnetic field lines, counteracting the deformation caused by the background shear flow. Linear analyses showed that the rotating flux-tube model describes the time-continuous evolution of fluctuations under shear flow as a single wavenumber mode. The formulation of the rotating flux-tube model makes explicit its mathematical correspondence to the Floquet theory. Nonlinear simulations demonstrated that the rotating flux-tube model can analyze the effects of background shear flow on turbulent transport.
{"title":"Rotating flux-tube model for local gyrokinetic simulations with background flow and magnetic shears","authors":"Shinya Maeyama , Tomo-Hiko Watanabe , Motoki Nakata , Masanori Nunami , Yuuichi Asahi , Akihiro Ishizawa","doi":"10.1016/j.jcp.2024.113595","DOIUrl":"10.1016/j.jcp.2024.113595","url":null,"abstract":"<div><div>We have developed a new computational method called the rotating flux-tube model that treats background shear flows in local gyrokinetic simulations. The method is based on extended magnetohydrodynamic ballooning mode theory. A coordinate transformation moves the flux-tube simulation domain along the sheared magnetic field lines, counteracting the deformation caused by the background shear flow. Linear analyses showed that the rotating flux-tube model describes the time-continuous evolution of fluctuations under shear flow as a single wavenumber mode. The formulation of the rotating flux-tube model makes explicit its mathematical correspondence to the Floquet theory. Nonlinear simulations demonstrated that the rotating flux-tube model can analyze the effects of background shear flow on turbulent transport.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113595"},"PeriodicalIF":3.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722497","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