论文标题
在基于错误的步长控制上，用于不连续的盖尔金方法，用于可压缩流体动力学
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
论文作者
论文摘要
我们研究了可压缩计算流体动力学（CFD）的显式runge-kutta方法的时间步长控制，包括Navier-Stokes方程和保护法的双曲线系统，例如Euler方程。我们证明，基于错误的方法在广泛的应用中很方便，并将它们与基于Courant-Friedrichs-Lewy（CFL）编号的更古典的步长控制进行了比较。我们的数值示例表明，基于错误的步长控制易于使用，稳健且有效，例如（初始）瞬态周期，复杂的几何形状，非线性冲击捕获方法以及使用非线性熵投影的方案。我们证明了这些属性的问题，这些问题涉及从熟悉的学术测试案例到具有两个不相交代码库的工业相关大规模计算，开源的Julia包Trixi.jl与普通Diffeq.jl以及基于PETSC的C/Fortran Code SSDC。
We study temporal step size control of explicit Runge-Kutta methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations. We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number. Our numerical examples show that error-based step size control is easy to use, robust, and efficient, e.g., for (initial) transient periods, complex geometries, nonlinear shock capturing approaches, and schemes that use nonlinear entropy projections. We demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases, the open source Julia packages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.
