Pub Date : 2024-11-19DOI: 10.1016/j.jcp.2024.113590
Luke Triplett, Jianfeng Lu
In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for path generation in this paper: a chain-based approach and a midpoint-based approach. The first biases the original dynamics to facilitate transitions, while the second mirrors splitting techniques and breaks down the original transition into smaller transitions. Numerical results of generated transition paths for the Müller potential and for Alanine dipeptide demonstrate the effectiveness of these approaches in both the data-rich and data-scarce regimes.
{"title":"Diffusion methods for generating transition paths","authors":"Luke Triplett, Jianfeng Lu","doi":"10.1016/j.jcp.2024.113590","DOIUrl":"10.1016/j.jcp.2024.113590","url":null,"abstract":"<div><div>In this work, we seek to simulate rare transitions between metastable states using score-based generative models. An efficient method for generating high-quality transition paths is valuable for the study of molecular systems since data is often difficult to obtain. We develop two novel methods for path generation in this paper: a chain-based approach and a midpoint-based approach. The first biases the original dynamics to facilitate transitions, while the second mirrors splitting techniques and breaks down the original transition into smaller transitions. Numerical results of generated transition paths for the Müller potential and for Alanine dipeptide demonstrate the effectiveness of these approaches in both the data-rich and data-scarce regimes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113590"},"PeriodicalIF":3.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706986","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 : 2024-11-19DOI: 10.1016/j.jcp.2024.113596
Maxime Jonval , Ibtihel Ben Gharbia , Clément Cancès , Thibault Faney , Quang-Huy Tran
Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used ad hoc treatments, we propose two reformulations of the single-phase chemical equilibrium problem which are in line with the spirit of preconditioning but whose actual aims are to guarantee a better stability of Newton's method. The first reformulation is a parametrization of the graph linking species mole fractions to their chemical potentials. The second is based on an augmented system where this relationship is relaxed for the iterates by means of a Cartesian representation. We theoretically prove the local quadratic convergence of Newton's method for both reformulations. From a numerical point of view, we demonstrate that the two techniques are accurate, allowing to compute equilibria with chemical species having very low concentrations. Moreover, the robustness of our methods combined with a globalization strategy is superior to that of the literature.
{"title":"Parametrization and Cartesian representation techniques for robust resolution of chemical equilibria","authors":"Maxime Jonval , Ibtihel Ben Gharbia , Clément Cancès , Thibault Faney , Quang-Huy Tran","doi":"10.1016/j.jcp.2024.113596","DOIUrl":"10.1016/j.jcp.2024.113596","url":null,"abstract":"<div><div>Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used <em>ad hoc</em> treatments, we propose two reformulations of the single-phase chemical equilibrium problem which are in line with the spirit of preconditioning but whose actual aims are to guarantee a better stability of Newton's method. The first reformulation is a parametrization of the graph linking species mole fractions to their chemical potentials. The second is based on an augmented system where this relationship is relaxed for the iterates by means of a Cartesian representation. We theoretically prove the local quadratic convergence of Newton's method for both reformulations. From a numerical point of view, we demonstrate that the two techniques are accurate, allowing to compute equilibria with chemical species having very low concentrations. Moreover, the robustness of our methods combined with a globalization strategy is superior to that of the literature.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113596"},"PeriodicalIF":3.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723645","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 : 2024-11-19DOI: 10.1016/j.jcp.2024.113589
Xuelian Bao , Chun Liu , Yiwei Wang
In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element method (FEM) discretization for the macroscopic fluid dynamics equation with a deterministic variational particle scheme for the microscopic Fokker-Planck equation. To address challenges arising from micro-macro coupling, we employ a discrete energetic variational approach to derive a coarse-grained micro-macro model with a particle approximation first and then develop a particle-FEM discretization for the coarse-grained model. The accuracy of the proposed method is evaluated for a Hookean dumbbell model in a Couette flow by comparing the computed velocity field with existing analytical solutions. We also use our method to study nonlinear FENE dumbbell models in different scenarios, such as extensional flow, pure shear flow, and lid-driven cavity flow. Numerical examples demonstrate that the proposed deterministic particle approach can accurately capture the various key rheological phenomena in the original FENE model, including hysteresis and δ-function-like spike behavior in extensional flows, velocity overshoot phenomenon in pure shear flows, symmetries breaking, vortex center shifting, and vortices weakening in lid-driven cavity flows, with a small number of particles.
{"title":"A deterministic–particle–based scheme for micro-macro viscoelastic flows","authors":"Xuelian Bao , Chun Liu , Yiwei Wang","doi":"10.1016/j.jcp.2024.113589","DOIUrl":"10.1016/j.jcp.2024.113589","url":null,"abstract":"<div><div>In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element method (FEM) discretization for the macroscopic fluid dynamics equation with a deterministic variational particle scheme for the microscopic Fokker-Planck equation. To address challenges arising from micro-macro coupling, we employ a discrete energetic variational approach to derive a coarse-grained micro-macro model with a particle approximation first and then develop a particle-FEM discretization for the coarse-grained model. The accuracy of the proposed method is evaluated for a Hookean dumbbell model in a Couette flow by comparing the computed velocity field with existing analytical solutions. We also use our method to study nonlinear FENE dumbbell models in different scenarios, such as extensional flow, pure shear flow, and lid-driven cavity flow. Numerical examples demonstrate that the proposed deterministic particle approach can accurately capture the various key rheological phenomena in the original FENE model, including hysteresis and <em>δ</em>-function-like spike behavior in extensional flows, velocity overshoot phenomenon in pure shear flows, symmetries breaking, vortex center shifting, and vortices weakening in lid-driven cavity flows, with a small number of particles.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113589"},"PeriodicalIF":3.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723644","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 : 2024-11-17DOI: 10.1016/j.jcp.2024.113587
Xiaojian Yang , Yajun Zhu , Chang Liu , Kun Xu
The multi-frequency radiation transport equation (RTE) system models the photon transport and the energy exchange process between the background material and different frequency photons. In this paper, the unified gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed to capture the multiscale non-equilibrium transport in different optical regimes. In the UGKWP, a multiscale evolution process is properly designed to obtain both non-equilibrium transport in the optically thin regime and thermal diffusion process in the optically thick regime automatically. At the same time, the coupled macroscopic energy equations for the photon and material are solved implicitly by the matrix-free source iteration method. With the wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity for different regime physics. In the optically thick regime, no particles will be sampled in the computational domain due to the intensive energy exchange between photon and background material, and the thermal diffusion solution for the photon transport will be recovered. While in the optically thin regime, stochastic particles will play a dominant role in the evolution and the non-equilibrium free transport of photon is automatically followed. In the frequency-dependent transport, the frequency carried by the simulating particle will be determined by a linear-frequency sampling strategy. In addition, to better resolve the sharp transition of opacity in the photon transport across a cell interface, the free streaming time of simulating particle in the UGKWP method will be reset when it passes through the interface. Moreover, the numerical relaxation time is properly defined to increase the particle proportion in the sharp opacity transition region in order to avoid numerical oscillation. Several typical test cases for the RTE system have been calculated to demonstrate the accuracy and reliability of the current frequency-dependent UGKWP method.
{"title":"Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation","authors":"Xiaojian Yang , Yajun Zhu , Chang Liu , Kun Xu","doi":"10.1016/j.jcp.2024.113587","DOIUrl":"10.1016/j.jcp.2024.113587","url":null,"abstract":"<div><div>The multi-frequency radiation transport equation (RTE) system models the photon transport and the energy exchange process between the background material and different frequency photons. In this paper, the unified gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed to capture the multiscale non-equilibrium transport in different optical regimes. In the UGKWP, a multiscale evolution process is properly designed to obtain both non-equilibrium transport in the optically thin regime and thermal diffusion process in the optically thick regime automatically. At the same time, the coupled macroscopic energy equations for the photon and material are solved implicitly by the matrix-free source iteration method. With the wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity for different regime physics. In the optically thick regime, no particles will be sampled in the computational domain due to the intensive energy exchange between photon and background material, and the thermal diffusion solution for the photon transport will be recovered. While in the optically thin regime, stochastic particles will play a dominant role in the evolution and the non-equilibrium free transport of photon is automatically followed. In the frequency-dependent transport, the frequency carried by the simulating particle will be determined by a linear-frequency sampling strategy. In addition, to better resolve the sharp transition of opacity in the photon transport across a cell interface, the free streaming time of simulating particle in the UGKWP method will be reset when it passes through the interface. Moreover, the numerical relaxation time is properly defined to increase the particle proportion in the sharp opacity transition region in order to avoid numerical oscillation. Several typical test cases for the RTE system have been calculated to demonstrate the accuracy and reliability of the current frequency-dependent UGKWP method.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113587"},"PeriodicalIF":3.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706985","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 : 2024-11-17DOI: 10.1016/j.jcp.2024.113575
Xi Deng , Zhen-hua Jiang , Chao Yan
Developing accurate, efficient and robust shock-capturing schemes on non-uniform grids remains challenging particularly when facing strong non-uniformity. Thus, we extend the unified normalised-variable diagram (UND) initially proposed by Deng (2023) [30] on uniform grids to non-uniform grids, and propose essentially non-oscillatory (ENO) and high-resolution regions in non-uniform grid UND. Based on the proposed UND, we formulate a high-resolution shock-capturing scheme termed ROUND (Reconstruction Operators on Unified-Normalise-variable Diagram) on non-uniform meshes. Unlike classic WENO (Weighted Essentially Non-Oscillatory) schemes applied to non-uniform grids, the ROUND scheme avoids the expensive calculation of smoothness indicators. The ROUND scheme is first applied to solve the scalar convection equation. The results reveal that the ROUND scheme significantly improves the numerical resolution and preserves the structure of the passively convected scalar compared to the TVD (Total Variation Diminishing) limiters. For capturing discontinuous solutions, the proposed ROUND scheme on non-uniform meshes surpasses the performance of the 5th-order WENO-JS scheme. The ROUND scheme is then integrated into discontinuous Galerkin (DG) with the FV subcell limiting method to enhance the numerical resolution at the subcell level while adhering to the discrete conservation law. The compactness and simplicity of the ROUND scheme on non-uniform grids are compatible with the DG method, known for its features such as compactness and flexibility of hp-refinement. The resulting DG method, utilising finite volume ROUND subcell limiting, is denoted as the DG/FV-ROUND scheme. To assess the accuracy and robustness of the DG/FV-ROUND scheme, we simulate high-speed compressible flows characterized by strong shock waves and small-scale flow structures. Comparative studies show the improved numerical resolution achieved by DG/FV-ROUND. Thus, this research demonstrates the efficacy and robustness of the ROUND scheme on non-uniform grids and affirms that incorporating high-resolution ROUND as subcell shock-capturing schemes can enhance the resolution of DG/FV methods.
{"title":"Efficient ROUND schemes on non-uniform grids applied to discontinuous Galerkin schemes with Godunov-type finite volume sub-cell limiting","authors":"Xi Deng , Zhen-hua Jiang , Chao Yan","doi":"10.1016/j.jcp.2024.113575","DOIUrl":"10.1016/j.jcp.2024.113575","url":null,"abstract":"<div><div>Developing accurate, efficient and robust shock-capturing schemes on non-uniform grids remains challenging particularly when facing strong non-uniformity. Thus, we extend the unified normalised-variable diagram (UND) initially proposed by Deng (2023) <span><span>[30]</span></span> on uniform grids to non-uniform grids, and propose essentially non-oscillatory (ENO) and high-resolution regions in non-uniform grid UND. Based on the proposed UND, we formulate a high-resolution shock-capturing scheme termed ROUND (Reconstruction Operators on Unified-Normalise-variable Diagram) on non-uniform meshes. Unlike classic WENO (Weighted Essentially Non-Oscillatory) schemes applied to non-uniform grids, the ROUND scheme avoids the expensive calculation of smoothness indicators. The ROUND scheme is first applied to solve the scalar convection equation. The results reveal that the ROUND scheme significantly improves the numerical resolution and preserves the structure of the passively convected scalar compared to the TVD (Total Variation Diminishing) limiters. For capturing discontinuous solutions, the proposed ROUND scheme on non-uniform meshes surpasses the performance of the 5th-order WENO-JS scheme. The ROUND scheme is then integrated into discontinuous Galerkin (DG) with the FV subcell limiting method to enhance the numerical resolution at the subcell level while adhering to the discrete conservation law. The compactness and simplicity of the ROUND scheme on non-uniform grids are compatible with the DG method, known for its features such as compactness and flexibility of hp-refinement. The resulting DG method, utilising finite volume ROUND subcell limiting, is denoted as the DG/FV-ROUND scheme. To assess the accuracy and robustness of the DG/FV-ROUND scheme, we simulate high-speed compressible flows characterized by strong shock waves and small-scale flow structures. Comparative studies show the improved numerical resolution achieved by DG/FV-ROUND. Thus, this research demonstrates the efficacy and robustness of the ROUND scheme on non-uniform grids and affirms that incorporating high-resolution ROUND as subcell shock-capturing schemes can enhance the resolution of DG/FV methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113575"},"PeriodicalIF":3.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706859","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}
Implicit time discretization in computational fluid dynamics dedicated to compute steady state solution of hypersonic flows was an intense field of research in the 70's-80's. It is suitable for computational efficiency to use implicit schemes that do not suffer from time step restriction to guarantee stability, unlike explicit ones. Unfortunately time step restriction is still required in practice, especially for stiff numerical test cases such as high Mach number flows around objects. A method introduced by Yee et al. (1985) [34] is commonly used to simulate computational fluid dynamics problems in an implicit fashion. However this method has no formal theoretical basis for systems of conservation laws. Consequently the practical time step is driven by a ad-hoc user-given profile. The purpose of this work is first to study the mathematical properties of such linearized implicit finite volume schemes to enlighten their weaknesses and exhibit more adequate linearization processes. We rely on the hyperbolicity of the Euler equations to establish a general framework to design implicit schemes. Secondly, we propose a correction of the system matrix to adapt to any given finite volume scheme. The obtained linearized implicit finite volume methods are more robust and less constrained with regards to ad-hoc user-given profile. Numerical results in 1D and 2D will provide evidences to confirm the analysis on relevant and challenging hypersonic test cases.
{"title":"Toward robust linear implicit schemes for steady state hypersonic flows","authors":"Benoît Cossart , Jean-Philippe Braeunig , Raphaël Loubère","doi":"10.1016/j.jcp.2024.113586","DOIUrl":"10.1016/j.jcp.2024.113586","url":null,"abstract":"<div><div>Implicit time discretization in computational fluid dynamics dedicated to compute steady state solution of hypersonic flows was an intense field of research in the 70's-80's. It is suitable for computational efficiency to use implicit schemes that do not suffer from time step restriction to guarantee stability, unlike explicit ones. Unfortunately time step restriction is still required in practice, especially for stiff numerical test cases such as high Mach number flows around objects. A method introduced by Yee et al. (1985) <span><span>[34]</span></span> is commonly used to simulate computational fluid dynamics problems in an implicit fashion. However this method has no formal theoretical basis for systems of conservation laws. Consequently the practical time step is driven by a ad-hoc user-given profile. The purpose of this work is first to study the mathematical properties of such linearized implicit finite volume schemes to enlighten their weaknesses and exhibit more adequate linearization processes. We rely on the hyperbolicity of the Euler equations to establish a general framework to design implicit schemes. Secondly, we propose a correction of the system matrix to adapt to any given finite volume scheme. The obtained linearized implicit finite volume methods are more robust and less constrained with regards to ad-hoc user-given profile. Numerical results in 1D and 2D will provide evidences to confirm the analysis on relevant and challenging hypersonic test cases.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113586"},"PeriodicalIF":3.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142706987","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 : 2024-11-17DOI: 10.1016/j.jcp.2024.113578
Mahmoud Shaqfa , Gary P.T. Choi , Guillaume Anciaux , Katrin Beyer
When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces because of the surface roughnesses. It is, therefore, crucial to accurately describe the morphology of rough surfaces, for instance, by extracting the fractal dimension and the so-called Hurst exponent, which is a typical signature of rough surfaces. This can be done using harmonic decomposition, which is easy for periodic and nominally flat surfaces since Fourier transforms allow fast and reliable decomposition. Yet, it remains a challenging task in the general curved and non-periodic cases, where more appropriate basis functions must be used. In this work, disk harmonics based on Fourier-Bessel basis functions are employed for decomposing open single-edge genus-0 surfaces (no holes) as a practical and fast alternative to characterise self-affine rough surfaces with the power Fourier-Bessel spectral density. An analytical relationship between the power spectrum density decay and the Hurst exponent is derived through an extension of the Wiener-Khinchin theorem in the special case where surfaces are assumed self-affine and isotropic. Finally, this approach is demonstrated to successfully measure the fractal dimension, Hurst exponent, without introducing typical biases coming from basis functions boundary conditions, surface discretisation or curvature of the surface patches. This work opens the path for contact mechanics studies based on the Fourier-Bessel spectral representation of curved and rough surface morphologies. All implementation details for this method are available under GNU LGPLv3 terms and conditions.
当两个物体接触时，由于表面粗糙度的原因，实际上只有一小部分表观面积参与产生接触力和摩擦力。因此，准确描述粗糙表面的形态至关重要，例如通过提取分形维度和所谓的赫斯特指数（粗糙表面的典型特征）。这可以通过谐波分解来实现，由于傅立叶变换可以快速可靠地进行分解，因此对于周期性和名义上平坦的表面来说，谐波分解很容易。然而，在一般的曲面和非周期性情况下，必须使用更合适的基函数，这仍然是一项具有挑战性的任务。在这项工作中，基于傅里叶-贝塞尔基函数的圆盘谐波被用来分解开放的单边 0 属表面（无孔），作为一种实用而快速的替代方法，用傅里叶-贝塞尔功率谱密度来表征自粗糙表面。在假设表面自成平面且各向同性的特殊情况下，通过对维纳-欣钦定理的扩展，得出了功率谱密度衰减与赫斯特指数之间的分析关系。最后，证明了这种方法可以成功测量分形维度和赫斯特指数，而不会引入基函数边界条件、表面离散化或表面斑块曲率带来的典型偏差。这项工作为基于曲面和粗糙表面形态的傅立叶-贝塞尔谱表示的接触力学研究开辟了道路。该方法的所有实施细节均根据 GNU LGPLv3 条款和条件提供。
{"title":"Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces","authors":"Mahmoud Shaqfa , Gary P.T. Choi , Guillaume Anciaux , Katrin Beyer","doi":"10.1016/j.jcp.2024.113578","DOIUrl":"10.1016/j.jcp.2024.113578","url":null,"abstract":"<div><div>When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces because of the surface roughnesses. It is, therefore, crucial to accurately describe the morphology of rough surfaces, for instance, by extracting the fractal dimension and the so-called <em>Hurst</em> exponent, which is a typical signature of rough surfaces. This can be done using harmonic decomposition, which is easy for periodic and nominally flat surfaces since <em>Fourier transforms</em> allow fast and reliable decomposition. Yet, it remains a challenging task in the general curved and non-periodic cases, where more appropriate basis functions must be used. In this work, disk harmonics based on Fourier-Bessel basis functions are employed for decomposing open single-edge genus-0 surfaces (no holes) as a practical and fast alternative to characterise self-affine rough surfaces with the power Fourier-Bessel spectral density. An analytical relationship between the power spectrum density decay and the Hurst exponent is derived through an extension of the Wiener-Khinchin theorem in the special case where surfaces are assumed self-affine and isotropic. Finally, this approach is demonstrated to successfully measure the fractal dimension, <em>Hurst</em> exponent, without introducing typical biases coming from basis functions boundary conditions, surface discretisation or curvature of the surface patches. This work opens the path for contact mechanics studies based on the Fourier-Bessel spectral representation of curved and rough surface morphologies. All implementation details for this method are available under GNU LGPLv3 terms and conditions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113578"},"PeriodicalIF":3.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723649","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 : 2024-11-17DOI: 10.1016/j.jcp.2024.113588
Gerald Warnecke
In 1961 Godunov wrote a very interesting seminal paper [24] on how to obtain positive symmetric systems of equations in the sense of Friedrichs [21]. The examples were Euler-Lagrange equations from the calculus of variations, equations of crystal optics and gas dynamics. This review is a survey of the method in application to the hyperbolic conservation laws of gas dynamics, the Euler equations.
{"title":"On Godunov's interesting class of systems - The symmetric hyperbolic Euler equations of gas dynamics","authors":"Gerald Warnecke","doi":"10.1016/j.jcp.2024.113588","DOIUrl":"10.1016/j.jcp.2024.113588","url":null,"abstract":"<div><div>In 1961 Godunov wrote a very interesting seminal paper <span><span>[24]</span></span> on how to obtain positive symmetric systems of equations in the sense of Friedrichs <span><span>[21]</span></span>. The examples were Euler-Lagrange equations from the calculus of variations, equations of crystal optics and gas dynamics. This review is a survey of the method in application to the hyperbolic conservation laws of gas dynamics, the Euler equations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"522 ","pages":"Article 113588"},"PeriodicalIF":3.8,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705741","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 : 2024-11-16DOI: 10.1016/j.jcp.2024.113566
Michael M. Crockatt , Andrew J. Christlieb , Cory D. Hauck
{"title":"Corrigendum to “Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods”","authors":"Michael M. Crockatt , Andrew J. Christlieb , Cory D. Hauck","doi":"10.1016/j.jcp.2024.113566","DOIUrl":"10.1016/j.jcp.2024.113566","url":null,"abstract":"","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"521 ","pages":"Article 113566"},"PeriodicalIF":3.8,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699579","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 : 2024-11-15DOI: 10.1016/j.jcp.2024.113579
Hyeokjoo Park , Gwanghyun Jo
In this work, we develop a physics-informed neural network based method to solve the nonlinear Poisson-Boltzmann (PB) equation. One challenge in predicting the solution of the PB equation arises from the Dirac-delta type singularities, which causes the solution to blow up near the singular charges. To manage this issue, we construct Green-type functions to handle the singular component of the solution. Subtracting these functions yields a regularized PB equation exhibiting discontinuity across the solute-solvent interface. To handle the discontinuities, we employ a continuous Sobolev extension for the solution of the regularized PB equation on each subdomain. By adding an augmentation variable to label the sub-regions, we are able to achieve a continuous extension of the regularized solution. Finally, the physics-informed neural network (PINN) is proposed, where the parameters are determined by a judiciously chosen loss functional. In this way, we propose a user-friendly efficient approximation for the PB equation without the necessity for any mesh generation or linearization process such as the Newton-Krylov iteration. The error estimates of the proposed PINN method are carried out. We prove that the error between the exact and neural network solutions can be bounded by the physics-informed loss functional, whose magnitude can be made arbitrarily small for appropriately trained neural networks with sufficiently many parameters. Several numerical experiments are provided to demonstrate the performance of the proposed PINN method.
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