Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables
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| Format: | Preprint |
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2025
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| _version_ | 1866908453971165184 |
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| author | Yao, Zhen Trenchea, Catalin Pei, Wenlong |
| author_facet | Yao, Zhen Trenchea, Catalin Pei, Wenlong |
| contents | Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Elsässer variables. We reduce the computational cost of the iterative non-linear solver, at each time step, by partitioning the coupled system into two subproblems of half size, solved in parallel. We prove that the iterations converge linearly, under a time step restriction similar to the one required in the full space-time error analysis. The variable step algorithm unconditionally conserves the energy, cross-helicity and magnetic helicity, and numerical solutions are second-order accurate in the $L^{2}$ and $H^{1}$-norms. The time adaptive mechanism, based on a local truncation error criterion, helps the variable step algorithm balance accuracy and time efficiency. Several numerical tests support the theoretical findings and verify the advantage of time adaptivity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_12700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables Yao, Zhen Trenchea, Catalin Pei, Wenlong Numerical Analysis Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Elsässer variables. We reduce the computational cost of the iterative non-linear solver, at each time step, by partitioning the coupled system into two subproblems of half size, solved in parallel. We prove that the iterations converge linearly, under a time step restriction similar to the one required in the full space-time error analysis. The variable step algorithm unconditionally conserves the energy, cross-helicity and magnetic helicity, and numerical solutions are second-order accurate in the $L^{2}$ and $H^{1}$-norms. The time adaptive mechanism, based on a local truncation error criterion, helps the variable step algorithm balance accuracy and time efficiency. Several numerical tests support the theoretical findings and verify the advantage of time adaptivity. |
| title | Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.12700 |