Pub Date : 2026-01-05DOI: 10.1016/j.jcp.2025.114644
Keji Liu , Jiaru Wang
This work addresses the inverse problem of simultaneously reconstructing trajectories and strengths of moving acoustic point sources, with applications in gesture recognition, underwater sonar, and sound simulation. Under practical assumptions including co-located source initiation and a few kinematic profiles, we establish uniqueness results for both source trajectories and strengths. The reconstruction of trajectories is formulated through ordinary differential equations, while the recovery of strengths is determined via a matrix-vector system at each time step using at most four sensors. To mitigate numerical instability from ill-conditioned matrices, we introduce a direct imaging method employing an efficient indicator function based solely on Euclidean norm computations, avoiding matrix inversion or iterative optimization. Numerical experiments demonstrate reliable simultaneous recovery of trajectories and strengths for multiple moving sources, confirming the effectiveness of the proposed method and practical utility for real-world acoustic sensing applications.
{"title":"Simultaneous reconstruction of the trajectories and strengths for moving acoustic point sources","authors":"Keji Liu , Jiaru Wang","doi":"10.1016/j.jcp.2025.114644","DOIUrl":"10.1016/j.jcp.2025.114644","url":null,"abstract":"<div><div>This work addresses the inverse problem of simultaneously reconstructing trajectories and strengths of moving acoustic point sources, with applications in gesture recognition, underwater sonar, and sound simulation. Under practical assumptions including co-located source initiation and a few kinematic profiles, we establish uniqueness results for both source trajectories and strengths. The reconstruction of trajectories is formulated through ordinary differential equations, while the recovery of strengths is determined via a matrix-vector system at each time step using at most four sensors. To mitigate numerical instability from ill-conditioned matrices, we introduce a direct imaging method employing an efficient indicator function based solely on Euclidean norm computations, avoiding matrix inversion or iterative optimization. Numerical experiments demonstrate reliable simultaneous recovery of trajectories and strengths for multiple moving sources, confirming the effectiveness of the proposed method and practical utility for real-world acoustic sensing applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114644"},"PeriodicalIF":3.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923628","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 : 2026-01-02DOI: 10.1016/j.jcp.2025.114635
Khemraj Gautam Kshetri , Amneet Pal Singh Bhalla , Nitesh Nama
We present a volume penalization technique for simulating acoustically-actuated flows in geometrically complex microchannels. Using a perturbation approach, the nonlinear response of an acoustically-actuated compressible Newtonian fluid moving over obstacles or flowing in a geometrically complex domain is segregated into two sub-problems: a harmonic first-order problem and a time-averaged second-order problem, where the latter utilizes forcing terms and boundary conditions arising from the first-order solution. This segregation results in two distinct volume penalized systems of equations. The no-slip boundary condition at the fluid-solid interface is enforced by prescribing a zero structure velocity for the first-order problem, while spatially varying Stokes drift—which depends on the gradient of the first-order solution—is prescribed as the structure velocity for the second-order problem. The harmonic first-order system is solved via MUMPS direct solver, whereas the steady state second-order system is solved iteratively using a novel projection method-based preconditioner. The preconditioned iterative solver for the second-order system is demonstrated to be highly effective and scalable with respect to increasing penalty force and grid resolution, respectively. A novel contour integration technique to evaluate the acoustic radiation force on an immersed object is also proposed. This technique circumvents the use of velocity derivatives within the smeared region. The contour integral is specifically tailored to Cartesian grids. Through a series of test cases featuring representative microfluidic geometries, we demonstrate excellent agreement between the volume penalized and body-fitted grid solutions for the primary first- and second-order fields as well as for the acoustic radiation force that depends on the gradients of these fields. We also identify suitable penalty factors and interfacial smearing widths to accurately capture the first- and second-order solutions. These results provide empirical evidence of the efficacy of the volume penalization method for simulating acoustic streaming problems that have commonly been analyzed using body-fitted methods in the acoustofluidic literature.
{"title":"Simulating acoustically-actuated flows in complex microchannels using the volume penalization technique","authors":"Khemraj Gautam Kshetri , Amneet Pal Singh Bhalla , Nitesh Nama","doi":"10.1016/j.jcp.2025.114635","DOIUrl":"10.1016/j.jcp.2025.114635","url":null,"abstract":"<div><div>We present a volume penalization technique for simulating acoustically-actuated flows in geometrically complex microchannels. Using a perturbation approach, the nonlinear response of an acoustically-actuated compressible Newtonian fluid moving over obstacles or flowing in a geometrically complex domain is segregated into two sub-problems: a harmonic first-order problem and a time-averaged second-order problem, where the latter utilizes forcing terms and boundary conditions arising from the first-order solution. This segregation results in two distinct volume penalized systems of equations. The no-slip boundary condition at the fluid-solid interface is enforced by prescribing a zero structure velocity for the first-order problem, while spatially varying Stokes drift—which depends on the gradient of the first-order solution—is prescribed as the structure velocity for the second-order problem. The harmonic first-order system is solved via MUMPS direct solver, whereas the steady state second-order system is solved iteratively using a novel projection method-based preconditioner. The preconditioned iterative solver for the second-order system is demonstrated to be highly effective and scalable with respect to increasing penalty force and grid resolution, respectively. A novel contour integration technique to evaluate the acoustic radiation force on an immersed object is also proposed. This technique circumvents the use of velocity derivatives within the smeared region. The contour integral is specifically tailored to Cartesian grids. Through a series of test cases featuring representative microfluidic geometries, we demonstrate excellent agreement between the volume penalized and body-fitted grid solutions for the primary first- and second-order fields as well as for the acoustic radiation force that depends on the gradients of these fields. We also identify suitable penalty factors and interfacial smearing widths to accurately capture the first- and second-order solutions. These results provide empirical evidence of the efficacy of the volume penalization method for simulating acoustic streaming problems that have commonly been analyzed using body-fitted methods in the acoustofluidic literature.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114635"},"PeriodicalIF":3.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974704","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 : 2026-01-02DOI: 10.1016/j.jcp.2025.114645
Qiling Gu , Wenlong Zhang , Zhidong Zhang
This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the L2-Tikhonov regularization method, we analyze its convergence under two different noise models, using noisy discrete spatial observations. By exploiting the spectral decomposition of the forward operator and introducing a noise separation technique into the variational framework, we establish error bounds for the reconstructed solution u and the source term f without requiring classical source conditions. Moreover, an expected convergence rate for the source error is derived in a weaker topology. We also extend the analysis to the fully discrete case with finite element discretization, showing that the overall error depends only on the noise level, regularization parameter, time step size, and spatial mesh size. These estimates provide a basis for selecting the optimal regularization parameter in a data-driven manner, without a priori information. Numerical experiments validate the theoretical results and demonstrate the efficiency of the proposed algorithm.
{"title":"Solving the inverse source problems for wave equation with final time measurements by a data driven approach","authors":"Qiling Gu , Wenlong Zhang , Zhidong Zhang","doi":"10.1016/j.jcp.2025.114645","DOIUrl":"10.1016/j.jcp.2025.114645","url":null,"abstract":"<div><div>This paper develops a discrete data-driven approach for solving the inverse source problem of the wave equation with final time measurements. Focusing on the <em>L</em><sup>2</sup>-Tikhonov regularization method, we analyze its convergence under two different noise models, using noisy discrete spatial observations. By exploiting the spectral decomposition of the forward operator and introducing a noise separation technique into the variational framework, we establish error bounds for the reconstructed solution <em>u</em> and the source term <em>f</em> without requiring classical source conditions. Moreover, an expected convergence rate for the source error is derived in a weaker topology. We also extend the analysis to the fully discrete case with finite element discretization, showing that the overall error depends only on the noise level, regularization parameter, time step size, and spatial mesh size. These estimates provide a basis for selecting the optimal regularization parameter in a data-driven manner, without a priori information. Numerical experiments validate the theoretical results and demonstrate the efficiency of the proposed algorithm.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114645"},"PeriodicalIF":3.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903989","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 : 2026-01-02DOI: 10.1016/j.jcp.2025.114643
Yixuan Zhang , Gang Bao
The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical non-imaging optics. Mathematically, it can be formulated as an optimization problem, which is exactly the optimal transportation problem (OT) when the target is in the far field. The gradient of OT is governed by the generalized Monge-Ampère equation that models the far-field reflector system. Based on the gradient, this work presents a Sobolev gradient descent method implemented within a finite element framework to solve the corresponding OT. Local convergence of the method is established and numerical examples are provided to demonstrate the effectiveness of the method.
{"title":"An optimal transport approach to the far-field reflector problem via Sobolev gradient descent","authors":"Yixuan Zhang , Gang Bao","doi":"10.1016/j.jcp.2025.114643","DOIUrl":"10.1016/j.jcp.2025.114643","url":null,"abstract":"<div><div>The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical non-imaging optics. Mathematically, it can be formulated as an optimization problem, which is exactly the optimal transportation problem (OT) when the target is in the far field. The gradient of OT is governed by the generalized Monge-Ampère equation that models the far-field reflector system. Based on the gradient, this work presents a Sobolev gradient descent method implemented within a finite element framework to solve the corresponding OT. Local convergence of the method is established and numerical examples are provided to demonstrate the effectiveness of the method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114643"},"PeriodicalIF":3.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923633","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 : 2026-01-01DOI: 10.1016/j.jcp.2025.114648
Beibei Li
In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary differential equations, we use high precision numerical solvers to generate training data and use a Transformer network to model the evolution of the spectral coefficients. We design two complementary sequence models for the evolution of spectral coefficients, a Fourier Spectral Transformer and an exponential time difference Transformer. The latter embeds the analytic linear propagator of the PDE through an exponential time differencing update, while a Transformer is used to learn the nonlinear contribution. We evaluate the proposed Transformer with Burgers’ equation, two-dimensional and three-dimensional incompressible Navier-Stokes equations. The numerical experiments show that the models achieve highly accurate long-term predictions from relatively limited training data, and that the exponential time difference Transformer exhibits improved stability and convergence. The proposed Transformer generalizes well to unseen data, bringing a promising paradigm for real time prediction and control of complex dynamical systems.
{"title":"The Fourier Spectral Transformer for efficient and generalizable nonlinear PDEs","authors":"Beibei Li","doi":"10.1016/j.jcp.2025.114648","DOIUrl":"10.1016/j.jcp.2025.114648","url":null,"abstract":"<div><div>In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary differential equations, we use high precision numerical solvers to generate training data and use a Transformer network to model the evolution of the spectral coefficients. We design two complementary sequence models for the evolution of spectral coefficients, a Fourier Spectral Transformer and an exponential time difference Transformer. The latter embeds the analytic linear propagator of the PDE through an exponential time differencing update, while a Transformer is used to learn the nonlinear contribution. We evaluate the proposed Transformer with Burgers’ equation, two-dimensional and three-dimensional incompressible Navier-Stokes equations. The numerical experiments show that the models achieve highly accurate long-term predictions from relatively limited training data, and that the exponential time difference Transformer exhibits improved stability and convergence. The proposed Transformer generalizes well to unseen data, bringing a promising paradigm for real time prediction and control of complex dynamical systems.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114648"},"PeriodicalIF":3.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923629","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 : 2025-12-31DOI: 10.1016/j.jcp.2025.114637
Antonio Ghidoni , Edoardo Mantecca , Gianmaria Noventa , David Pasquale
The aim of this paper is to describe, validate and assess an explicit wall function implementation for the high-order spatial discretization of the Reynolds-Averaged Navier-Stokes and turbulence model equations. Wall functions are used to increase the computational efficiency of the solvers for numerical simulations, reducing the need for high quality computational meshes with fine near-wall spatial resolution. An explicit power-law to model the velocity profile of the flow in the boundary layer allows the proposed formulation to avoid iterative computations and ensures enhanced computational efficiency and robustness. These are demonstrated on different test cases with turbulent flows and adiabatic wall modelled boundaries. The accuracy of the numerical solutions is preserved up to a non dimensional height of the first element adjacent to the wall of 320 with a drastic computing time reduction. The high-order spatial discretization and the proposed formulation of wall function pave the way for numerical simulation of complex industrial applications with very coarse near-wall spatial resolution.
{"title":"Assessment of an explicit wall function implementation for the high-order discontinuous Galerkin solution of the RANS and k−ω turbulence model equations","authors":"Antonio Ghidoni , Edoardo Mantecca , Gianmaria Noventa , David Pasquale","doi":"10.1016/j.jcp.2025.114637","DOIUrl":"10.1016/j.jcp.2025.114637","url":null,"abstract":"<div><div>The aim of this paper is to describe, validate and assess an explicit wall function implementation for the high-order spatial discretization of the Reynolds-Averaged Navier-Stokes and <span><math><mrow><mi>k</mi><mspace></mspace><mo>−</mo><mspace></mspace><mi>ω</mi></mrow></math></span> turbulence model equations. Wall functions are used to increase the computational efficiency of the solvers for numerical simulations, reducing the need for high quality computational meshes with fine near-wall spatial resolution. An explicit power-law to model the velocity profile of the flow in the boundary layer allows the proposed formulation to avoid iterative computations and ensures enhanced computational efficiency and robustness. These are demonstrated on different test cases with turbulent flows and adiabatic wall modelled boundaries. The accuracy of the numerical solutions is preserved up to a non dimensional height of the first element adjacent to the wall of 320 with a drastic computing time reduction. The high-order spatial discretization and the proposed formulation of wall function pave the way for numerical simulation of complex industrial applications with very coarse near-wall spatial resolution.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114637"},"PeriodicalIF":3.8,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903986","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}
Updated Lagrangian smoothed particle hydrodynamics (SPH) for solid dynamics is often plagued by numerical instabilities, particularly hourglass modes that produce unphysical zigzag patterns. While recent essentially non-hourglass (SPH-ENOG) and generalized non-hourglass (SPH-GNOG) formulations have improved stability, they suffer from poor angular momentum conservation, limiting their accuracy in rotational problems. To overcome this, this paper presents two angular-momentum enhanced non-hourglass formulations. First, we enhance the SPH-ENOG method with rotation matrices derived from Rodrigues’ formula, creating SPH-ENOG-A for elastic materials, which explicitly accounts for rigid rotations during time integration, thereby significantly enhancing angular momentum conservation. To strictly enforce linear momentum conservation, the average of the rotation matrices is computed and applied to each particle. We then extend this approach to reformulate the corrective term in SPH-GNOG, yielding SPH-GNOG-A—a unified method for both elastic and plastic materials that not only improves angular momentum conservation but also eliminates prior dependencies on material-specific coefficients. Validated against elastic (oscillating plates, spinning solids) and plastic (Taylor bars, high-velocity impacts) benchmarks, our methods retain the hourglass-free stability, convergence, and accuracy of their predecessors while achieving a significant leap in angular momentum conservation.
用于固体动力学的更新拉格朗日光滑粒子流体动力学（SPH）经常受到数值不稳定性的困扰，特别是产生非物理之字形的沙漏模式。虽然最近的基本非沙漏（SPH-ENOG）和广义非沙漏（SPH-GNOG）配方提高了稳定性，但它们的角动量守恒性差，限制了它们在旋转问题中的精度。为了克服这个问题，本文提出了两种角动量增强的非沙漏公式。首先，我们利用Rodrigues公式导出的旋转矩阵对SPH-ENOG方法进行了改进，创建了弹性材料的SPH-ENOG- a，该方法在时间积分过程中明确考虑了刚性旋转，从而显著提高了角动量守恒。为了严格执行线性动量守恒，计算旋转矩阵的平均值并将其应用于每个粒子。然后，我们将该方法扩展到SPH-GNOG中重新制定校正项，从而得到SPH-GNOG- a -一种适用于弹性和塑性材料的统一方法，该方法不仅改善了角动量守恒，而且消除了对材料特定系数的先前依赖。经过弹性（振荡板，旋转固体）和塑料（泰勒杆，高速撞击）基准的验证，我们的方法保留了其前辈的无沙漏稳定性，收敛性和准确性，同时实现了角动量守恒的重大飞跃。
{"title":"Angular-momentum enhanced non-hourglass formulation for SPH solid dynamics","authors":"Shuaihao Zhang , Jidong Zhao , Honghu Zhu , Xiangyu Hu","doi":"10.1016/j.jcp.2025.114646","DOIUrl":"10.1016/j.jcp.2025.114646","url":null,"abstract":"<div><div>Updated Lagrangian smoothed particle hydrodynamics (SPH) for solid dynamics is often plagued by numerical instabilities, particularly hourglass modes that produce unphysical zigzag patterns. While recent essentially non-hourglass (SPH-ENOG) and generalized non-hourglass (SPH-GNOG) formulations have improved stability, they suffer from poor angular momentum conservation, limiting their accuracy in rotational problems. To overcome this, this paper presents two angular-momentum enhanced non-hourglass formulations. First, we enhance the SPH-ENOG method with rotation matrices derived from Rodrigues’ formula, creating SPH-ENOG-A for elastic materials, which explicitly accounts for rigid rotations during time integration, thereby significantly enhancing angular momentum conservation. To strictly enforce linear momentum conservation, the average of the rotation matrices is computed and applied to each particle. We then extend this approach to reformulate the corrective term in SPH-GNOG, yielding SPH-GNOG-A—a unified method for both elastic and plastic materials that not only improves angular momentum conservation but also eliminates prior dependencies on material-specific coefficients. Validated against elastic (oscillating plates, spinning solids) and plastic (Taylor bars, high-velocity impacts) benchmarks, our methods retain the hourglass-free stability, convergence, and accuracy of their predecessors while achieving a significant leap in angular momentum conservation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114646"},"PeriodicalIF":3.8,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903988","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 : 2025-12-31DOI: 10.1016/j.jcp.2025.114642
Bangti Jin, Fengru Wang, Jun Zou
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary information, a heterogeneously regularized Dirichlet-to-Neumann map to enhance the near-orthogonality of probing functions, and a stabilization-correction strategy to ensure the numerical stability. The resulting method is remarkably robust with respect to measurement noise, is flexible with the measurement configuration, enjoys provable stability guarantee, and achieves enhanced resolution for recovering inhomogeneities. Numerical experiments in electrical impedance tomography, diffuse optical tomography, and cardiac electrophysiology show its effectiveness in accurately reconstructing the locations and geometries of inhomogeneities.
{"title":"A stable iterative direct sampling method for elliptic inverse problems with partial Cauchy data","authors":"Bangti Jin, Fengru Wang, Jun Zou","doi":"10.1016/j.jcp.2025.114642","DOIUrl":"10.1016/j.jcp.2025.114642","url":null,"abstract":"<div><div>We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary information, a heterogeneously regularized Dirichlet-to-Neumann map to enhance the near-orthogonality of probing functions, and a stabilization-correction strategy to ensure the numerical stability. The resulting method is remarkably robust with respect to measurement noise, is flexible with the measurement configuration, enjoys provable stability guarantee, and achieves enhanced resolution for recovering inhomogeneities. Numerical experiments in electrical impedance tomography, diffuse optical tomography, and cardiac electrophysiology show its effectiveness in accurately reconstructing the locations and geometries of inhomogeneities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114642"},"PeriodicalIF":3.8,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923623","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 : 2025-12-31DOI: 10.1016/j.jcp.2025.114649
Jan Nordström
In previous work, we derived new energy and entropy stable open boundary conditions and implementation techniques for linear and nonlinear initial boundary value problems. These boundary procedures result in estimates bounded by external data only. Interestingly, these new boundary conditions generalize the well-known classical characteristic boundary conditions for linear problems to the nonlinear setting. We discuss the similarities and differences between these two boundary procedures and point out the advantages with the new procedures. In particular we show that the new boundary conditions bound solutions to both linear and nonlinear initial boundary value problems and can be implemented both strongly and weakly.
{"title":"Linear and nonlinear boundary conditions: What’s the difference?","authors":"Jan Nordström","doi":"10.1016/j.jcp.2025.114649","DOIUrl":"10.1016/j.jcp.2025.114649","url":null,"abstract":"<div><div>In previous work, we derived new energy and entropy stable open boundary conditions and implementation techniques for linear and nonlinear initial boundary value problems. These boundary procedures result in estimates bounded by external data only. Interestingly, these new boundary conditions generalize the well-known classical characteristic boundary conditions for linear problems to the nonlinear setting. We discuss the similarities and differences between these two boundary procedures and point out the advantages with the new procedures. In particular we show that the new boundary conditions bound solutions to both linear and nonlinear initial boundary value problems and can be implemented both strongly and weakly.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114649"},"PeriodicalIF":3.8,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974764","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 : 2025-12-31DOI: 10.1016/j.jcp.2025.114641
Samuel W. Jones , Colin P. McNally , Meritt Reynolds
Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. We present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.
{"title":"A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics","authors":"Samuel W. Jones , Colin P. McNally , Meritt Reynolds","doi":"10.1016/j.jcp.2025.114641","DOIUrl":"10.1016/j.jcp.2025.114641","url":null,"abstract":"<div><div>Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of compressible resistive magnetohydrodynamics. The method is built around a finite volume formulation of the equations in which a Riemann solver is used to compute fluxes on the faces between grid cells, and a face-centered constrained transport formulation of the induction equation. The small time step problem associated with the cut cells is avoided by always computing fluxes on the faces and edges of the Cartesian mesh. We extend the method to model a moving interface between two materials with different properties using a ghost-fluid approach, and show some preliminary results including shock-wave-driven and magnetically-driven dynamical compressions of magnetohydrostatic equilibria. We present a thorough verification of the method and show that it converges at second order in the absence of discontinuities, and at first order with a discontinuity in material properties.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114641"},"PeriodicalIF":3.8,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923632","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}
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