Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0026
Haoxiang Huang, Vigor Yang null, Yingjie Liu
{"title":"Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems","authors":"Haoxiang Huang, Vigor Yang null, Yingjie Liu","doi":"10.4208/cicp.oa-2023-0026","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0026","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2023-0050
Jiahe Yang null, W. Ying
{"title":"A Fast Cartesian Grid-Based Integral Equation Method for Unbounded Interface Problems with Non-Homogeneous Source Terms","authors":"Jiahe Yang null, W. Ying","doi":"10.4208/cicp.oa-2023-0050","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0050","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43103721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2022-0310
Richard Archibald, Feng Bao null, J. Yong
{"title":"A Sample-Wise Data Driven Control Solver for the Stochastic Optimal Control Problem with Unknown Model Parameters","authors":"Richard Archibald, Feng Bao null, J. Yong","doi":"10.4208/cicp.oa-2022-0310","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0310","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46601656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
. In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the x - and y -directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.
{"title":"A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow","authors":"Zhiqiang Zeng, Chengliang Feng, Xiaotao Zhang, Shengtao Zhang null, Tiegang Liu","doi":"10.4208/cicp.oa-2022-0314","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0314","url":null,"abstract":". In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the x - and y -directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46286289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2022-0233
Wenqiang Xiao, Bo Gong, Junshan Lin null, Jiguang Sun
{"title":"Band Structure Calculations of Dispersive Photonic Crystals in 3D using Holomorphic Operator Functions","authors":"Wenqiang Xiao, Bo Gong, Junshan Lin null, Jiguang Sun","doi":"10.4208/cicp.oa-2022-0233","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0233","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49652728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2022-0092
Zhongling Li, Li Liu null, Jun-bo Cheng
{"title":"A One-Dimensional Second-Order Cell-Centered Lagrangian Scheme Satisfying the Entropy Condition","authors":"Zhongling Li, Li Liu null, Jun-bo Cheng","doi":"10.4208/cicp.oa-2022-0092","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0092","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47037271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2022-0271
Zhicheng Hu null, Guanghan Li
{"title":"An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow","authors":"Zhicheng Hu null, Guanghan Li","doi":"10.4208/cicp.oa-2022-0271","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0271","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2023-0058
Honghui Wang, Lu Lu, Shiji Song null, Gao Huang
{"title":"Learning Specialized Activation Functions for Physics-Informed Neural Networks","authors":"Honghui Wang, Lu Lu, Shiji Song null, Gao Huang","doi":"10.4208/cicp.oa-2023-0058","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0058","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2023-06-01DOI: 10.4208/cicp.oa-2022-0270
Yifei Wan null, Yinhua Xia
. For steady Euler equations in complex boundary domains, high-order shock-capturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian grids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-order finite difference hybrid WENO scheme to simulate steady Euler equations, and the same fifth-order WENO extrapolation methods are developed to handle the curved boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform the tangential derivatives along the curved solid wall boundary. This hybrid WENO scheme is robust for steady-state convergence and maintains high-order accuracy in the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows that this hybrid WENO scheme has low dispersion and dissipation errors. Numerical examples are presented to validate the high-order accuracy and robust performance of the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.
{"title":"A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids","authors":"Yifei Wan null, Yinhua Xia","doi":"10.4208/cicp.oa-2022-0270","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0270","url":null,"abstract":". For steady Euler equations in complex boundary domains, high-order shock-capturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian grids to achieve uniform high-order accuracy. In this paper, we utilize a fifth-order finite difference hybrid WENO scheme to simulate steady Euler equations, and the same fifth-order WENO extrapolation methods are developed to handle the curved boundary. The values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary, involving normal derivatives acquired by the simplified inverse Lax-Wendroff procedure. Both equivalent expressions involving curvature and numerical differentiation are utilized to transform the tangential derivatives along the curved solid wall boundary. This hybrid WENO scheme is robust for steady-state convergence and maintains high-order accuracy in the smooth region even with the solid wall boundary condition. Besides, the essentially non-oscillation property is achieved. The numerical spectral analysis also shows that this hybrid WENO scheme has low dispersion and dissipation errors. Numerical examples are presented to validate the high-order accuracy and robust performance of the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45229733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}
. Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures. We propose a multiscale data-driven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic materials. Based on the sparse multiscale experimental data, the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm. A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different microstructures. And a dense stress-stretch relation dataset is generated by training a neural network through the FE results. Further, a generic invariant representation of strain energy function (SEF) is proposed with a parameter set being implicitly expressed by artificial neural networks (SANN), which describes the hyperelastic properties of heterogeneous materials with different microstructures. A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant
{"title":"Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data","authors":"Rui He, Junzhi Cui, Zihao Yang, Jieqiong Zhang null, Xiaofei Guan","doi":"10.4208/cicp.oa-2023-0098","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0098","url":null,"abstract":". Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures. We propose a multiscale data-driven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic materials. Based on the sparse multiscale experimental data, the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm. A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different microstructures. And a dense stress-stretch relation dataset is generated by training a neural network through the FE results. Further, a generic invariant representation of strain energy function (SEF) is proposed with a parameter set being implicitly expressed by artificial neural networks (SANN), which describes the hyperelastic properties of heterogeneous materials with different microstructures. A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41985774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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