AI 中文总结
本文提出一种半隐式 IMEX 有限体积格式，适用于任意马赫数、支持通用状态方程，可保结构与压力正性，经多类基准测试验证了其精度、稳定性与激波捕捉能力。
AI 中文摘要
我们提出了一种保守、保结构的有限体积格式，用于理想磁流体力学（MHD），该格式可确保压力正性、适用于所有马赫数与阿尔文马赫数区间，且能处理一般非线性状态方程。该格式根据特征波尺度将 MHD 系统拆分为三个子系统：流体输运的平流部分、速度场耦合的磁场部分，以及压力-速度耦合的压力部分。非线性平流项采用显式处理，其余两个子系统采用隐式处理，从而得到温和的、基于速度的 CFL 条件，大量数值证据支持该条件成立，这使得该格式适用于气压主导或磁压主导的区间，以及不可压缩极限情况。隐式离散化得到的压力方程在理想气体和一般热力学的低马赫极限下会简化为椭圆形式。压力正性通过对压力-内能关系的局部守恒保持修改来确保，避免了后验截断，同时保持了守恒性。通过约束输运精确满足散度为零约束。该格式采用 IMEX Runge-Kutta 时间积分、显式通量的 TVD 重构以及隐式项的中心离散化，实现了二阶精度。通过大量基准测试对该格式进行了验证，包括高马赫与低马赫区间、强磁化流动，以及一维和二维的标准 MHD 激波问题，验证结果表明该格式具有精度、稳定性和出色的激波捕捉能力。
英文摘要
We present a conservative, structure-preserving, finite-volume scheme for ideal MHD that ensures pressure positivity, remains applicable across all Mach and Alfven regimes, and handles general nonlinear equations of state. The scheme splits the MHD system into three sub-systems according to characteristic wave scales: an advective part for hydrodynamic transport, a magnetic part for velocity-field coupling, and a pressure part for pressure-velocity coupling. Nonlinear advective terms are explicit, while the other two sub-systems are implicit, yielding a mild, velocity-based CFL condition that is supported by extensive numerical evidence. This makes the scheme suitable for gas-pressure or magnetic-pressure dominated regimes and the incompressible limit. The implicit discretisation gives a pressure equation that reduces to an elliptic form in the low-Mach limit for ideal gases and general thermodynamics. Pressure positivity is ensured via a local conservation-preserving modification of the pressure-internal-energy relation, avoiding a posteriori clipping while preserving conservation. The divergence-free constraint is enforced exactly via constrained transport. Second-order accuracy is achieved with an IMEX Runge-Kutta time integration, TVD reconstruction for explicit fluxes, and central discretisation for implicit terms. The scheme is validated against numerous benchmarks, including high- and low-Mach regimes, strongly magnetised flows, and standard MHD shock problems in 1D and 2D, demonstrating accuracy, stability, and excellent shock-capturing.
