Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations

doi:10.1007/s42967-025-00492-4

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (3): 1171-1206.doi: 10.1007/s42967-025-00492-4

Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations

Jaya Agnihotri¹, Deepak Bhoriya², Harish Kumar¹, Praveen Chandrashekar³, Dinshaw S. Balsara^2,4

1. Department of Mathematics, Indian Institute of Technology Delhi, Delhi, India;
2. Physics Department, University of Notre Dame, Notre Dame, IN, USA;
3. Centre for Applicable Mathematics, TIFR, Bangalore, India;
4. ACMS, University of Notre Dame, Notre Dame, IN, USA

收稿日期:2024-09-11 修回日期:2025-02-14 出版日期:2026-06-20 发布日期:2026-05-29
通讯作者: Jaya Agnihotri, Email: jayaagnihotri96@gmail.com E-mail:jayaagnihotri96@gmail.com
基金资助:
The work of Harish Kumar is supported in parts by the VAJRA (Grant No. VJR/2018/000129) by the Department of Science and Technology, Government of India. Harish Kumar and Jaya Agnihotri acknowledge the support of the FIST (Grant No. SR/FST/MS-1/2019/45) by the Department of Science and Technology, Government of India. The work of Praveen Chandrashekar is supported by the Department of Atomic Energy, Government of India (Grant No. 12-R&D-TFR-5.01-0520).

Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations

Jaya Agnihotri¹, Deepak Bhoriya², Harish Kumar¹, Praveen Chandrashekar³, Dinshaw S. Balsara^2,4

1. Department of Mathematics, Indian Institute of Technology Delhi, Delhi, India;
2. Physics Department, University of Notre Dame, Notre Dame, IN, USA;
3. Centre for Applicable Mathematics, TIFR, Bangalore, India;
4. ACMS, University of Notre Dame, Notre Dame, IN, USA

Received:2024-09-11 Revised:2025-02-14 Online:2026-06-20 Published:2026-05-29
Contact: Jaya Agnihotri, Email: jayaagnihotri96@gmail.com E-mail:jayaagnihotri96@gmail.com
Supported by:
This work was supported by the National Natural Science Foundation of China (No. 12001013).

摘要/Abstract

摘要： Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics (RHD) with Maxwell’s equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing numerical schemes for the model, the divergence constraints are ignored, or Maxwell’s equations are reformulated as perfectly hyperbolic Maxwell’s (PHM) equations by introducing additional equations for correction potentials. In the latter case, the divergence constraints are preserved only as the limiting case. In this article, we present second-order numerical schemes that preserve the divergence constraints for electric and magnetic fields at the discrete level. The schemes are based on using a multidimensional Riemann solver at the vertices of the cells to define the numerical fluxes on the edges. The second-order accuracy is obtained by reconstructing the electromagnetic fields at the corners using a MinMod limiter. The discretization of Maxwell’s equations can be combined with any consistent and stable discretization of the fluid parts. In particular, we consider entropy-stable schemes for the fluid part. The resulting schemes are second-order accurate, entropy stable, and preserve the divergence constraints of the electromagnetic fields. We use explicit and Implicit-Explicit-based (IMEX-based) time discretizations. We then test these schemes using several one- and two-dimensional test cases. We also compare the divergence constraint errors of the proposed schemes with schemes having no divergence constraints treatment and schemes based on the PHM-based divergence cleaning.

关键词: Two-fluid relativistic plasma flows, Divergence constraints preserving schemes, Implicit-Explicit (IMEX) schemes, Multidimensional Riemann solvers

Abstract: Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics (RHD) with Maxwell’s equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing numerical schemes for the model, the divergence constraints are ignored, or Maxwell’s equations are reformulated as perfectly hyperbolic Maxwell’s (PHM) equations by introducing additional equations for correction potentials. In the latter case, the divergence constraints are preserved only as the limiting case. In this article, we present second-order numerical schemes that preserve the divergence constraints for electric and magnetic fields at the discrete level. The schemes are based on using a multidimensional Riemann solver at the vertices of the cells to define the numerical fluxes on the edges. The second-order accuracy is obtained by reconstructing the electromagnetic fields at the corners using a MinMod limiter. The discretization of Maxwell’s equations can be combined with any consistent and stable discretization of the fluid parts. In particular, we consider entropy-stable schemes for the fluid part. The resulting schemes are second-order accurate, entropy stable, and preserve the divergence constraints of the electromagnetic fields. We use explicit and Implicit-Explicit-based (IMEX-based) time discretizations. We then test these schemes using several one- and two-dimensional test cases. We also compare the divergence constraint errors of the proposed schemes with schemes having no divergence constraints treatment and schemes based on the PHM-based divergence cleaning.

Key words: Two-fluid relativistic plasma flows, Divergence constraints preserving schemes, Implicit-Explicit (IMEX) schemes, Multidimensional Riemann solvers

中图分类号:

Jaya Agnihotri, Deepak Bhoriya, Harish Kumar, Praveen Chandrashekar, Dinshaw S. Balsara. Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations[J]. Communications on Applied Mathematics and Computation, 2026, 8(3): 1171-1206.

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Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations

Second-Order Divergence Constraint Preserving Schemes for Two-Fluid Relativistic Plasma Flow Equations

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