Communications on Applied Mathematics and Computation最新文献

{"title":"An Alternative Finite Difference WENO-Like Scheme with Physical Constraint Preservation for Divergence-Preserving Hyperbolic Systems.","authors":"Dinshaw S Balsara, Deepak Bhoriya, Chi-Wang Shu","doi":"10.1007/s42967-025-00517-y","DOIUrl":"https://doi.org/10.1007/s42967-025-00517-y","url":null,"abstract":"<p><p>Alternative finite difference Weighted Essentially Non-Oscillatory (AFD-WENO) schemes allow us to very efficiently update hyperbolic systems even in complex geometries. Recent innovations in AFD-WENO methods allow us to treat hyperbolic systems with non-conservative products almost as efficiently as conservation laws. However, some PDE systems, like computational electrodynamics (CED), magnetohydrodynamics (MHD), and relativistic magnetohydrodynamics (RMHD), have involution constraints that require divergence-free or divergence-preserving evolution of vector fields. In such situations, a Yee-style collocation of variables proves indispensable, and that collocation is retained in this work. In previous works, only higher order finite volume (FV) discretization of such involution-constrained systems was possible. In this work, we show that substantially more efficient AFD-WENO methods have been extended to encompass divergence-preserving hyperbolic PDEs. Our method retains the Yee-style collocation of normal components of the divergence-free/preserving vector field. However, the variables that require zone-centered evolution are evolved with AFD-WENO methods. Since those variables make up the bulk of the primal variables for the PDE of interest, this results in substantial savings in computational complexity. Even the volumetric reconstruction of the divergence-free/preserving vector field is bypassed. Instead, we realize that any divergence-preserving update of a vector field must have a general form. This general form looks closely like the familiar induction equation that is well known in CED or MHD. We exploit the generality of that form to extract the edge-centered variables that are needed in the update of the facially averaged vector field components. The two-dimensional (2D) Riemann solver is used to provide us with multidimensionally stabilized versions of these update terms. The generality of our approach is demonstrated by the fact that problems in CED, MHD, and RMHD can all be solved by the same general AFD-WENO algorithm that is presented here. Spatial accuracies up to the ninth order of accuracy are demonstrated. Several stringent test problems from CED, MHD, and RMHD are shown. We also show that the algorithm takes well to the physical constraint-preserving (PCP) formulation of AFD-WENO schemes that was presented by the authors. The efficient and time-explicit PCP strategy for divergence-preserving PDEs that we have presented here extends the applicability of our method to very stringent MHD and RMHD problems.</p>","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"8 5","pages":"1730-1798"},"PeriodicalIF":1.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13588913/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149009006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Three-Dimensional Tumor Growth Model and Its Boundary Instability","authors":"Jianguo Liu, Thomas P. Witelski, Xiaoqian Xu, J. S. Zhang","doi":"10.1007/s42967-024-00443-5","DOIUrl":"https://doi.org/10.1007/s42967-024-00443-5","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"7 3","pages":"1034-1073"},"PeriodicalIF":0.0,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147903248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws","authors":"Antonio Baeza, Rosa Donat, A. Martínez-Gavara","doi":"10.1007/s42967-023-00332-3","DOIUrl":"https://doi.org/10.1007/s42967-023-00332-3","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"5 3","pages":"1-23"},"PeriodicalIF":1.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods","authors":"Ben Burnett, S. Gottlieb, Zachary J. Grant","doi":"10.1007/s42967-023-00315-4","DOIUrl":"https://doi.org/10.1007/s42967-023-00315-4","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"10 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138950994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Finite Difference Scheme for the Fractional Laplacian on Non-uniform Grids","authors":"A. M. Vargas","doi":"10.1007/s42967-023-00323-4","DOIUrl":"https://doi.org/10.1007/s42967-023-00323-4","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138967400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Class of Simple, General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems","authors":"S. Busto, M. Dumbser","doi":"10.1007/s42967-023-00307-4","DOIUrl":"https://doi.org/10.1007/s42967-023-00307-4","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"95 10","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138999387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conforming P3 Divergence-Free Finite Elements for the Stokes Equations on Subquadrilateral Triangular Meshes","authors":"Shangyou Zhang","doi":"10.1007/s42967-023-00335-0","DOIUrl":"https://doi.org/10.1007/s42967-023-00335-0","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes","authors":"Xiu Ye, Shangyou Zhang","doi":"10.1007/s42967-023-00330-5","DOIUrl":"https://doi.org/10.1007/s42967-023-00330-5","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"1 1‐2","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139005480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The L2-1σ/LDG Method for the Caputo Diffusion Equation with a Variable Coefficient","authors":"Qiaoqiao Dai, Dongxia Li","doi":"10.1007/s42967-023-00326-1","DOIUrl":"https://doi.org/10.1007/s42967-023-00326-1","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"74 10","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138596174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of Dynamic Pressure on the Shock Structure and Sub-shock Formation in a Mixture of Polyatomic Gases","authors":"Tommaso Ruggeri, S. Taniguchi","doi":"10.1007/s42967-023-00320-7","DOIUrl":"https://doi.org/10.1007/s42967-023-00320-7","url":null,"abstract":"","PeriodicalId":29916,"journal":{"name":"Communications on Applied Mathematics and Computation","volume":"82 8","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138606237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}