论文标题
通用PNPM方案的后验子细胞有限量限制：从气体学到相对论磁性水力动力学的应用
A posteriori subcell finite volume limiter for general PNPM schemes: applications from gasdynamics to relativistic magnetohydrodynamics
论文作者
论文摘要
在这项工作中，我们考虑了所谓的ADER PNPM方案的一般家族，用于具有\ textIt {Nutyary}高度准确性的高光偏微分方程的数值解。 在[Dumbser等人，JCP，2008]中引入了一步PNPM方案的家族，代表了经典高阶有限量（FV）方案（n = 0）的统一框架，这是通常的不连续的Galerkin（DG）方法（n = m），以及一类新的ISMED MEDIDERMED MEDIDER MEDIST MEDIDER MEDIDERMED MEDMED MEDMERMED MIMMED SCONSONS A BREBRID SCONSONS A BRIDID MIMMED MIMMED MIMBRID SCONSONS a a sembrId sembrid schembrid semss a a s a M> n的分段多项式数据。在所有情况下，M> = n> 0的PNPM方案在Godunov的意义上是线性的，因此在考虑以不连续性为特征的现象时，出现虚假振荡，甚至会破坏模拟。因此，在本文中，我们提出了一种新的简单，健壮且准确的后验子细胞有限体积限制策略，该策略对整个PNPM方案有效。仅在需要的情况下，即在冲击或其他不连续性的附近激活子电池FV限制器，并且能够维持基础高阶PNPM方案的分辨率，这是由于使用每个空间尺寸的2N+1个子电池的优质子网格。 该论文包含针对不同双曲线PDE系统的广泛测试用例，这些系统在自适应笛卡尔网格（AMR）上求解，这些系统在平滑和不连续问题上都显示了该方法的功能，以及其适用性的广泛范围。测试范围从经典MHD上的可压缩煤气动力学到相对论的磁流失动力学。
In this work, we consider the general family of the so called ADER PNPM schemes for the numerical solution of hyperbolic partial differential equations with \textit{arbitrary} high order of accuracy in space and time. The family of one-step PNPM schemes was introduced in [Dumbser et al., JCP, 2008] and represents a unified framework for classical high order Finite Volume (FV) schemes (N=0), the usual Discontinuous Galerkin (DG) methods (N=M), as well as a new class of intermediate hybrid schemes for which a reconstruction operator of degree M is applied over piecewise polynomial data of degree N with M>N. In all cases with M >= N > 0 the PNPM schemes are linear in the sense of Godunov, thus when considering phenomena characterized by discontinuities, spurious oscillations may appear and even destroy the simulation. Therefore, in this paper we present a new simple, robust and accurate a posteriori subcell finite volume limiting strategy that is valid for the entire class of PNPM schemes. The subcell FV limiter is activated only where it is needed, i.e. in the neighborhood of shocks or other discontinuities, and is able to maintain the resolution of the underlying high order PNPM schemes, due to the use of a rather fine subgrid of 2N+1 subcells per space dimension. The paper contains a wide set of test cases for different hyperbolic PDE systems, solved on adaptive Cartesian meshes (AMR) that show the capabilities of the proposed method both on smooth and discontinuous problems, as well as the broad range of its applicability. The tests range from compressible gasdynamics over classical MHD to relativistic magnetohydrodynamics.
