MPI-AMRVAC：一个并行的、网格自适应的PDE工具包
MPI-AMRVAC: a parallel, grid-adaptive PDE toolkit
摘要：
我们报告我们的开源，块网格自适应框架MPI-AMRVAC，这是一个通用的工具包，特别是双曲/抛物偏微分方程（PDE）的最新增加。应用传统上集中在冲击为主，磁化等离子体动力学描述的牛顿或特殊相对论（磁）流体力学，但其通用的设计很容易扩展到不同的PDE系统。在这里，我们展示了涵盖任何维标量到系统偏微分方程的应用，例如Korteweg-de Vries解决方案概括了孤立子行为的早期发现、圆形或方形水池中的浅水应用、流体动力学收敛测试以及具有挑战性的计算流体和等离子体动力学应用。最近增加了一个并行多重网格求解器开辟了新的途径，椭圆约束或刚性源项发挥核心作用。这里通过求解几个多维反应扩散型方程来说明这一点。我们记录的最低要求添加一个新的物理模块由任何非线性PDE系统，使它可以直接受益于代码的灵活性，结合各种时间和空间离散化方案。MPI-AMRVAC通过GitHub分发，可用于在笛卡尔、圆柱或球形坐标系中执行1D、1.5D、2D、2.5D或3D模拟，使用并行域分解或利用完全动态块四叉树-八叉树网格。
英文摘要：
We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC, which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs). Applications traditionally focused on shock-dominated, magnetized plasma dynamics described by either Newtonian or special relativistic (magneto)hydrodynamics, but its versatile design easily extends to different PDE systems. Here, we demonstrate applications covering any-dimensional scalar to system PDEs, with e.g. Korteweg-de Vries solutions generalizing early findings on soliton behaviour, shallow water applications in round or square pools, hydrodynamic convergence tests as well as challenging computational fluid and plasma dynamics applications. The recent addition of a parallel multigrid solver opens up new avenues where also elliptic constraints or stiff source terms play a central role. This is illustrated here by solving several multi-dimensional reaction-diffusion-type equations. We document the minimal requirements for adding a new physics module governed by any nonlinear PDE system, such that it can directly benefit from the code flexibility in combining various temporal and spatial discretisation schemes. Distributed through GitHub, MPI-AMRVAC can be used to perform 1D, 1.5D, 2D, 2.5D or 3D simulations in Cartesian, cylindrical or spherical coordinate systems, using parallel domain-decomposition, or exploiting fully dynamic block quadtree-octree grids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
