Pub Date : 2022-02-26DOI: 10.2140/camcos.2022.17.43
C. Enaux, S. Guisset, C. Lasuen, G. Samba
{"title":"Numerical methods for coupling multigroup radiation with ion and electron temperatures","authors":"C. Enaux, S. Guisset, C. Lasuen, G. Samba","doi":"10.2140/camcos.2022.17.43","DOIUrl":"https://doi.org/10.2140/camcos.2022.17.43","url":null,"abstract":"","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88395779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-22DOI: 10.2140/camcos.2021.16.99
J. Guerra, P. Ullrich
{"title":"Spectral steady-state solutions to the 2D compressible Euler equations for cross-mountain flows","authors":"J. Guerra, P. Ullrich","doi":"10.2140/camcos.2021.16.99","DOIUrl":"https://doi.org/10.2140/camcos.2021.16.99","url":null,"abstract":"","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"8 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88935007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-04DOI: 10.2140/camcos.2019.14.175
T. Kang, Ran Wang, Huai Zhang
{"title":"Potential field formulation based on decomposition of the electric field for a nonlinear induction hardening model","authors":"T. Kang, Ran Wang, Huai Zhang","doi":"10.2140/camcos.2019.14.175","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.175","url":null,"abstract":"","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"125 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86031174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-13DOI: 10.2140/camcos.2020.15.1
Emmanuel Motheau, J. Wakefield
The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method perform better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.
{"title":"Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows","authors":"Emmanuel Motheau, J. Wakefield","doi":"10.2140/camcos.2020.15.1","DOIUrl":"https://doi.org/10.2140/camcos.2020.15.1","url":null,"abstract":"The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method perform better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2019-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86244705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-10-30DOI: 10.2140/camcos.2018.13.337
Chris Kavouklis,Phillip Colella
{"title":"Computation of volume potentials on structured grids with the method of local corrections","authors":"Chris Kavouklis,Phillip Colella","doi":"10.2140/camcos.2018.13.337","DOIUrl":"https://doi.org/10.2140/camcos.2018.13.337","url":null,"abstract":"","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"IE-31 4","pages":"337-368"},"PeriodicalIF":2.1,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-26DOI: 10.2140/camcos.2019.14.207
M. Cameron, Shuo Yang
The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general. We propose a methodology for computing the quasipotential for highly dissipative and chaotic systems built on the example of Lorenz'63 with an added stochastic term. It is based on the ordered line integral method, a Dijkstra-like quasipotential solver, and combines 3D computations in whole regions, a dimensional reduction technique, and 2D computations on radial meshes on manifolds or their unions. Our collection of source codes is available on M. Cameron's web page and on GitHub.
{"title":"Computing the quasipotential for highly\u0000dissipative and chaotic SDEs an application to stochastic Lorenz’63","authors":"M. Cameron, Shuo Yang","doi":"10.2140/camcos.2019.14.207","DOIUrl":"https://doi.org/10.2140/camcos.2019.14.207","url":null,"abstract":"The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general. \u0000We propose a methodology for computing the quasipotential for highly dissipative and chaotic systems built on the example of Lorenz'63 with an added stochastic term. It is based on the ordered line integral method, a Dijkstra-like quasipotential solver, and combines 3D computations in whole regions, a dimensional reduction technique, and 2D computations on radial meshes on manifolds or their unions. Our collection of source codes is available on M. Cameron's web page and on GitHub.","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"46 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2018-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82748092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}