Pub Date : 2025-01-10DOI: 10.1016/j.jcp.2025.113731
Y. Pan , P.-O. Persson
We introduce the concept of half-closed nodes for nodal discontinuous Galerkin (DG) discretisations. Unlike more commonly used closed nodes in DG, where on every element nodes are placed on all of its boundaries, half-closed nodes only require nodes to be placed on a subset of the element's boundaries. The effect of using different nodes on DG operator sparsity is studied and we find in particular for there to be no difference in the sparsity pattern of the Laplace operator whether closed or half-closed nodes are used. On quadrilateral/hexahedral elements we use the Gauss-Radau points as the half-closed nodes of choice, which we demonstrate is able to speed up DG operator assembly in addition to leverage previously known superconvergence results. We also discuss in this work some linear solver techniques commonly used for Finite Element or discontinuous Galerkin methods such as static condensation and block-based methods, and how they can be applied to half-closed DG discretisations.
{"title":"Half-closed discontinuous Galerkin discretisations","authors":"Y. Pan , P.-O. Persson","doi":"10.1016/j.jcp.2025.113731","DOIUrl":"10.1016/j.jcp.2025.113731","url":null,"abstract":"<div><div>We introduce the concept of half-closed nodes for nodal discontinuous Galerkin (DG) discretisations. Unlike more commonly used closed nodes in DG, where on every element nodes are placed on all of its boundaries, half-closed nodes only require nodes to be placed on a subset of the element's boundaries. The effect of using different nodes on DG operator sparsity is studied and we find in particular for there to be no difference in the sparsity pattern of the Laplace operator whether closed or half-closed nodes are used. On quadrilateral/hexahedral elements we use the Gauss-Radau points as the half-closed nodes of choice, which we demonstrate is able to speed up DG operator assembly in addition to leverage previously known superconvergence results. We also discuss in this work some linear solver techniques commonly used for Finite Element or discontinuous Galerkin methods such as static condensation and block-based methods, and how they can be applied to half-closed DG discretisations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113731"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131778","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}
This study introduces an order-lifted inversion/retrieval method for implementing high-order schemes within the framework of an unstructured-mesh-based finite-volume method. This method defines a special representation called the data order-lifted inversion of neighbor cells (DOLINC) differential, which transforms the degrees of freedom of wide templates into differentials of various orders stored in local grid cells. Furthermore, to retrieve the original far-field information without bias during the reconstruction/interpolation of face values, the corresponding accurate inversion formulas are derived based on the defined DOLINC differentials. The order-lifted inversion method can be applied to multi-dimensional polyhedral-mesh solvers by considering the influence of grid non-uniformity on high-order schemes. It seamlessly accommodates multi-process parallel computing for high-order methods without requiring special consideration for the boundary interface. This method not only enhances the numerical accuracy of second-order finite-volume methods, but also demonstrates a significant computational-speed advantage over similar methods. A series of benchmark cases, including the linear advection, Burgers, and Euler equations, are comprehensively validated to assess the practical performance of the method. The results indicate that the unstructured-mesh high-order schemes implemented based on this method achieve theoretical accuracy in practical computations and substantially reduce computational costs compared with methods that increase grid resolution.
{"title":"Order-lifted data inversion/retrieval method of neighbor cells to implement general high-order schemes in unstructured-mesh-based finite-volume solution framework","authors":"Hao Guo, Boxing Hu, Peixue Jiang, Xiaofeng Ma, Yinhai Zhu","doi":"10.1016/j.jcp.2025.113735","DOIUrl":"10.1016/j.jcp.2025.113735","url":null,"abstract":"<div><div>This study introduces an order-lifted inversion/retrieval method for implementing high-order schemes within the framework of an unstructured-mesh-based finite-volume method. This method defines a special representation called the data order-lifted inversion of neighbor cells (DOLINC) differential, which transforms the degrees of freedom of wide templates into differentials of various orders stored in local grid cells. Furthermore, to retrieve the original far-field information without bias during the reconstruction/interpolation of face values, the corresponding accurate inversion formulas are derived based on the defined DOLINC differentials. The order-lifted inversion method can be applied to multi-dimensional polyhedral-mesh solvers by considering the influence of grid non-uniformity on high-order schemes. It seamlessly accommodates multi-process parallel computing for high-order methods without requiring special consideration for the boundary interface. This method not only enhances the numerical accuracy of second-order finite-volume methods, but also demonstrates a significant computational-speed advantage over similar methods. A series of benchmark cases, including the linear advection, Burgers, and Euler equations, are comprehensively validated to assess the practical performance of the method. The results indicate that the unstructured-mesh high-order schemes implemented based on this method achieve theoretical accuracy in practical computations and substantially reduce computational costs compared with methods that increase grid resolution.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113735"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143132053","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113730
Victor Churchill
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional non-uniform grids. We address limitations of previous work on data-driven flow map learning in the sense that we focus on noisy and limited data to move toward data collection scenarios in real-world applications. Leveraging recent work on modeling PDEs in modal and nodal spaces, we present a neural network structure that is suitable for PDE modeling with noisy and limited data available only on a subset of the state variables or computational domain. In particular, spatial grid-point measurements are reduced using a learned linear transformation, after which the dynamics are learned in this reduced basis before being transformed back out to the nodal space. This approach yields a drastically reduced parameterization of the neural network compared with previous flow map models for nodal space learning. This allows for rapid high-resolution simulations, enabled by smaller training data sets and reduced training times.
{"title":"Principal component flow map learning of PDEs from incomplete, limited, and noisy data","authors":"Victor Churchill","doi":"10.1016/j.jcp.2025.113730","DOIUrl":"10.1016/j.jcp.2025.113730","url":null,"abstract":"<div><div>We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional non-uniform grids. We address limitations of previous work on data-driven flow map learning in the sense that we focus on noisy and limited data to move toward data collection scenarios in real-world applications. Leveraging recent work on modeling PDEs in modal and nodal spaces, we present a neural network structure that is suitable for PDE modeling with noisy and limited data available only on a subset of the state variables or computational domain. In particular, spatial grid-point measurements are reduced using a learned linear transformation, after which the dynamics are learned in this reduced basis before being transformed back out to the nodal space. This approach yields a drastically reduced parameterization of the neural network compared with previous flow map models for nodal space learning. This allows for rapid high-resolution simulations, enabled by smaller training data sets and reduced training times.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113730"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131968","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113727
Xiaodong Wang, Shuai Yang
A new numerical method, which is based on the coupling between semi-Lagrangian meshfree method and two-phase lattice Boltzmann (LB) model, is developed for incompressible two-phase flows. Two LB equations, one is for solving the Cahn-Hilliard equation for capturing interface and the other is for solving the two-phase Navier-Stokes equations for flow field, are involved. In view of the pure convection property of the LB equations, the semi-Lagrangian meshfree method we proposed before is used to solve them. This is a fully meshfree method that inherits all the distinct advantages of meshfree method and traditional LB method. Firstly, it generalizes the LB method to the meshfree case and breaks through the limitation of uniform mesh. Secondly, it eliminates the coupling of temporal and spatial step sizes and thus is easier to meeting specified accuracy requirements. Thirdly, it gives full play to the advantages of LB model in interface capture and parallel computation. Finally, it can solve two-phase flow problems in complex geometric domains by using non-uniform spatial discretization, and maintain high accuracy and stability. Three benchmark tests show the new method possesses an excellent mass conservation ability on both uniform and non-uniform node arrangements. Subsequently, the method is applied to several two-phase flow problems by using non-uniform meshfree nodes. The results agree very well with the analytical or reference solutions even for the rather extreme simulation cases. The good performance of this method suggests it is a powerful tool for solving two-phase flows.
{"title":"A semi-Lagrangian meshfree lattice Boltzmann method for incompressible two-phase flows","authors":"Xiaodong Wang, Shuai Yang","doi":"10.1016/j.jcp.2025.113727","DOIUrl":"10.1016/j.jcp.2025.113727","url":null,"abstract":"<div><div>A new numerical method, which is based on the coupling between semi-Lagrangian meshfree method and two-phase lattice Boltzmann (LB) model, is developed for incompressible two-phase flows. Two LB equations, one is for solving the Cahn-Hilliard equation for capturing interface and the other is for solving the two-phase Navier-Stokes equations for flow field, are involved. In view of the pure convection property of the LB equations, the semi-Lagrangian meshfree method we proposed before is used to solve them. This is a fully meshfree method that inherits all the distinct advantages of meshfree method and traditional LB method. Firstly, it generalizes the LB method to the meshfree case and breaks through the limitation of uniform mesh. Secondly, it eliminates the coupling of temporal and spatial step sizes and thus is easier to meeting specified accuracy requirements. Thirdly, it gives full play to the advantages of LB model in interface capture and parallel computation. Finally, it can solve two-phase flow problems in complex geometric domains by using non-uniform spatial discretization, and maintain high accuracy and stability. Three benchmark tests show the new method possesses an excellent mass conservation ability on both uniform and non-uniform node arrangements. Subsequently, the method is applied to several two-phase flow problems by using non-uniform meshfree nodes. The results agree very well with the analytical or reference solutions even for the rather extreme simulation cases. The good performance of this method suggests it is a powerful tool for solving two-phase flows.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113727"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131713","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113734
Mohsen Lahooti , Edward Laughton , Junjie Ye , Chris D. Cantwell , David Moxey
The high-fidelity modelling of geometry which rotates or translates is a key requirement in fluid mechanics applications, enabling the simulation of parts such as rotors and pressure cascades. These prescribed motions can be imposed through the movement of the mesh representing the problem, where an interface is constructed across the nonconformal interface, bridging the static and moving regions of the mesh. The challenge is maintaining the solution accuracy across this interface, which will involve nonconformal elements on its sides due to the sliding meshes, while having a robust and efficient approach for complex interfaces. This work uses a point-to-point interpolation technique for such sliding interfaces, leveraging the high-order discontinuous Galerkin method for discretising governing equations and the Arbitrary Lagrangian-Eulerian (ALE) method in handling sliding meshes. With its straightforward and efficient approach, the point-to-point interpolation method has an advantage over other approaches in dealing with the complex interface while having excellent accuracy in preserving the discrete geometric conservation law (DGCL), as demonstrated in this study. Linear and non-linear hyperbolic systems, including the compressible Euler and Navier-Stokes equations, are considered with detailed analysis demonstrating the point-to-point method's accuracy using several examples and under various settings in the context of high-order methods for flow problems.
{"title":"Discontinuous Galerkin simulation of sliding geometries using a point-to-point interpolation technique","authors":"Mohsen Lahooti , Edward Laughton , Junjie Ye , Chris D. Cantwell , David Moxey","doi":"10.1016/j.jcp.2025.113734","DOIUrl":"10.1016/j.jcp.2025.113734","url":null,"abstract":"<div><div>The high-fidelity modelling of geometry which rotates or translates is a key requirement in fluid mechanics applications, enabling the simulation of parts such as rotors and pressure cascades. These prescribed motions can be imposed through the movement of the mesh representing the problem, where an interface is constructed across the nonconformal interface, bridging the static and moving regions of the mesh. The challenge is maintaining the solution accuracy across this interface, which will involve nonconformal elements on its sides due to the sliding meshes, while having a robust and efficient approach for complex interfaces. This work uses a point-to-point interpolation technique for such sliding interfaces, leveraging the high-order discontinuous Galerkin method for discretising governing equations and the Arbitrary Lagrangian-Eulerian (ALE) method in handling sliding meshes. With its straightforward and efficient approach, the point-to-point interpolation method has an advantage over other approaches in dealing with the complex interface while having excellent accuracy in preserving the discrete geometric conservation law (DGCL), as demonstrated in this study. Linear and non-linear hyperbolic systems, including the compressible Euler and Navier-Stokes equations, are considered with detailed analysis demonstrating the point-to-point method's accuracy using several examples and under various settings in the context of high-order methods for flow problems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113734"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131712","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113726
Tyler Chang , Andrew Gillette , Romit Maulik
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.
{"title":"Leveraging interpolation models and error bounds for verifiable scientific machine learning","authors":"Tyler Chang , Andrew Gillette , Romit Maulik","doi":"10.1016/j.jcp.2025.113726","DOIUrl":"10.1016/j.jcp.2025.113726","url":null,"abstract":"<div><div>Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113726"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131715","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113742
Huanfeng Yang , Guangqing Long , Yiming Ren , Shan Zhao
A new Augmented Matched Interface and Boundary (AMIB) method with the fast Fourier transform (FFT) acceleration is proposed for three-dimensional (3D) Helmholtz interface problems. This method inherits the merits of the existing FFT-AMIB method for Poisson interface problems, such as the FFT efficiency and effective treatments of different boundary conditions including Dirichlet, Neumann, Robin and their arbitrary combinations. However, the previous FFT-AMIB method is not applicable to Helmholtz interface problems due to the discontinuous wavenumbers in the Helmholtz equation. To overcome this difficulty, the Helmholtz interface problem is decomposed into two subproblems, each defined on a subdomain with the zero-padding on the other. Consequently, the original problem can be transformed into two elliptic interface problems, which allow the FFT inversion. Besides the domain decomposition, the new AMIB method possesses several novel features. In resolving interfaces with complex shapes, the jump conditions are enforced along Cartesian directions, instead of along normal directions as in the existing ray-casting AMIB scheme. Various fourth order corner treatments have been developed in the Cartesian Matched Interface and Boundary (MIB) scheme to ensure robustness. Moreover, an optimized iterative algorithm combining the GMRES and BiCGSTAB has been designed in solving the auxiliary variables involved in the Schur complement solution of the augmented system. Extensive numerical experiments show that the method achieves fourth order accuracy for both solutions and gradients, with an overall complexity of for a uniform grid.
{"title":"An augmented fourth order domain-decomposed method with fast algebraic solvers for three-dimensional Helmholtz interface problems","authors":"Huanfeng Yang , Guangqing Long , Yiming Ren , Shan Zhao","doi":"10.1016/j.jcp.2025.113742","DOIUrl":"10.1016/j.jcp.2025.113742","url":null,"abstract":"<div><div>A new Augmented Matched Interface and Boundary (AMIB) method with the fast Fourier transform (FFT) acceleration is proposed for three-dimensional (3D) Helmholtz interface problems. This method inherits the merits of the existing FFT-AMIB method for Poisson interface problems, such as the FFT efficiency and effective treatments of different boundary conditions including Dirichlet, Neumann, Robin and their arbitrary combinations. However, the previous FFT-AMIB method is not applicable to Helmholtz interface problems due to the discontinuous wavenumbers in the Helmholtz equation. To overcome this difficulty, the Helmholtz interface problem is decomposed into two subproblems, each defined on a subdomain with the zero-padding on the other. Consequently, the original problem can be transformed into two elliptic interface problems, which allow the FFT inversion. Besides the domain decomposition, the new AMIB method possesses several novel features. In resolving interfaces with complex shapes, the jump conditions are enforced along Cartesian directions, instead of along normal directions as in the existing ray-casting AMIB scheme. Various fourth order corner treatments have been developed in the Cartesian Matched Interface and Boundary (MIB) scheme to ensure robustness. Moreover, an optimized iterative algorithm combining the GMRES and BiCGSTAB has been designed in solving the auxiliary variables involved in the Schur complement solution of the augmented system. Extensive numerical experiments show that the method achieves fourth order accuracy for both solutions and gradients, with an overall complexity of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span> for a <span><math><mi>n</mi><mo>×</mo><mi>n</mi><mo>×</mo><mi>n</mi></math></span> uniform grid.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113742"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131965","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 : 2025-01-10DOI: 10.1016/j.jcp.2025.113736
L. Pacaut , S. Chaillat , J.F. Mercier , G. Serre
In the naval industry many applications require to study the behavior of a penetrable obstacle embedded in water, notably in presence of a turbulent flow. Such configuration is encountered in particular when noise is scattered by two-phase fluids, e.g., turbulent flows with air bubbles. Fast and efficient numerical methods are required to compute this scattering in the presence of realistic 3D geometries, such as bubble curtains. In [1], we have developed a very efficient approach in the case of a rigid obstacle of arbitrary shape, excited by a turbulent flow. It is based on the numerical evaluation of tailored Green's functions. Here we extend this fast method to the case of a penetrable obstacle. It is not a straightforward extension and we propose two main contributions. First, tailored Green's functions for a fluid-fluid coupled problem are derived theoretically and determined numerically. Second, we show the need of a regularized Boundary Integral formulation to obtain these Green's functions accurately in all configurations. Finally, we illustrate the efficiency of the method on various applications related to the scattering by multiple bubbles.
{"title":"Efficient boundary integral method to evaluate the acoustic scattering from coupled fluid-fluid problems excited by multiple sources","authors":"L. Pacaut , S. Chaillat , J.F. Mercier , G. Serre","doi":"10.1016/j.jcp.2025.113736","DOIUrl":"10.1016/j.jcp.2025.113736","url":null,"abstract":"<div><div>In the naval industry many applications require to study the behavior of a penetrable obstacle embedded in water, notably in presence of a turbulent flow. Such configuration is encountered in particular when noise is scattered by two-phase fluids, e.g., turbulent flows with air bubbles. Fast and efficient numerical methods are required to compute this scattering in the presence of realistic 3D geometries, such as bubble curtains. In <span><span>[1]</span></span>, we have developed a very efficient approach in the case of a rigid obstacle of arbitrary shape, excited by a turbulent flow. It is based on the numerical evaluation of tailored Green's functions. Here we extend this fast method to the case of a penetrable obstacle. It is not a straightforward extension and we propose two main contributions. First, tailored Green's functions for a fluid-fluid coupled problem are derived theoretically and determined numerically. Second, we show the need of a regularized Boundary Integral formulation to obtain these Green's functions accurately in all configurations. Finally, we illustrate the efficiency of the method on various applications related to the scattering by multiple bubbles.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113736"},"PeriodicalIF":3.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131967","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 : 2025-01-09DOI: 10.1016/j.jcp.2025.113723
Prasanna Salasiya, Bojan B. Guzina
We develop an effective computational tool for simulating the scattering of one-dimensional (1D) waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media, which allows us to describe the wavefield in each segment in terms of the “left” and “right” (propagating or evanescent) Bloch waves. For a given periodic medium and frequency of oscillations, the latter are computed by solving the quadratic eigenvalue problem (QEP) which seeks the (real- or complex-valued) wavenumber – and affiliated eigenstate – of a Bloch wave. In this way the scattering problem is reduced to a low-dimensional algebraic problem, solved via the transfer matrix approach, that seeks the amplitudes of the featured Bloch waves (two per segment), amplitude of the reflected wave, and that of the transmitted wave. Such an approach inherently caters for an optimal filter (e.g. rainbow trap) design as it enables rapid exploration of the design space with respect to segment (i) permutations (with or without repetition), (ii) cut lengths, and (iii) cut offsets relative to the mother periodic media. Specifically, under (i)–(iii) the Bloch eigenstates remain invariant, so that only the transfer matrices need to be recomputed. The reduced order model is found to be in excellent agreement with numerical simulations. Example simulations demonstrate 40x computational speedup when optimizing a 1D filter for minimum transmission via a genetic algorithm (GA) approach that entails trial configurations. Relative to the classical rainbow trap design where the unit cells of the mother periodic media are arranged in a “linear” fashion according to their dispersive characteristics, the GA-optimized (rearranged) configuration yields a 40% reduction in filter transmissibility over the target frequency range, for the same filter thickness.
{"title":"A simple tool for the optimization of 1D phononic and photonic bandgap filters","authors":"Prasanna Salasiya, Bojan B. Guzina","doi":"10.1016/j.jcp.2025.113723","DOIUrl":"10.1016/j.jcp.2025.113723","url":null,"abstract":"<div><div>We develop an effective computational tool for simulating the scattering of one-dimensional (1D) waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media, which allows us to describe the wavefield in each segment in terms of the “left” and “right” (propagating or evanescent) Bloch waves. For a given periodic medium and frequency of oscillations, the latter are computed by solving the quadratic eigenvalue problem (QEP) which seeks the (real- or complex-valued) wavenumber – and affiliated eigenstate – of a Bloch wave. In this way the scattering problem is reduced to a low-dimensional algebraic problem, solved via the transfer matrix approach, that seeks the amplitudes of the featured Bloch waves (two per segment), amplitude of the reflected wave, and that of the transmitted wave. Such an approach inherently caters for an optimal filter (e.g. rainbow trap) design as it enables rapid exploration of the design space with respect to segment (i) permutations (with or without repetition), (ii) cut lengths, and (iii) cut offsets relative to the mother periodic media. Specifically, under (i)–(iii) the Bloch eigenstates remain invariant, so that only the transfer matrices need to be recomputed. The reduced order model is found to be in excellent agreement with numerical simulations. Example simulations demonstrate 40x computational speedup when optimizing a 1D filter for minimum transmission via a genetic algorithm (GA) approach that entails <span><math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></math></span> trial configurations. Relative to the classical rainbow trap design where the unit cells of the mother periodic media are arranged in a “linear” fashion according to their dispersive characteristics, the GA-optimized (rearranged) configuration yields a 40% reduction in filter transmissibility over the target frequency range, for the same filter thickness.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"524 ","pages":"Article 113723"},"PeriodicalIF":3.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131711","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 : 2025-01-09DOI: 10.1016/j.jcp.2024.113714
Sergiu Coseru , Sébastien Tanguy , Pierre Freton , Jean-Jacques Gonzalez , Annafederica Urbano , Marie Bibal , Gauthier Bourdon
Immersed Boundary Methods (IBM) are a practical class of methods that enable fluid computations in complex geometry while keeping a structured mesh. Most of the existing IBM have been developed in the framework of incompressible solvers, despite their significant interest to perform simulations in more complex configurations requiring a compressible solver. In the last years, pressure-based solvers met a growing interest to perform numerical simulations of compressible flows, due to their attractive features, as removing the stability condition on the acoustic time step, and being asymptotically preserving of the incompressible regime when the Mach number tends to zero. As this class of compressible solvers share many common features with classical projection methods for incompressible flows, our objective in this paper is to present an adaptation of an efficient and accurate IBM developed for an incompressible solver by Ng et al. in [1] to a pressure-based compressible solver recently published by Urbano et al. in [2]. The proposed algorithm benefits of the attractive properties of the original IBM proposed in [1] while being able to undertake simulations in much more complex configurations. In particular, we will present validations and illustrations of the proposed solver in various configurations as free-convection flows, acoustic waves propagating in a variable section pipe or interacting with a solid obstacle, as well as the description of a thermal plasma during an electric arc discharge in a gas.
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