论文标题
非静态垂直切片方程的兼容有限元离散化
A compatible finite element discretisation for the nonhydrostatic vertical slice equations
论文作者
论文摘要
我们在近距到最低的阶（即压力空间是双线性不连续函数），为垂直切片可压缩的欧拉方程提供了兼容的有限元离散化。这些方程是在时间上使用完全隐式的时间播放方案在时间上进行集成的，该方案是使用LinesMoother预处理的单片GMRE求解的。线条仅涉及局部操作，因此适用于并行的域分解。它允许任意较大的时间段，但迭代计数以courant数字在较大的数字限制的情况下进行线性缩放。使用Firedrake和PETSC的添加剂Schwarz预处理框架实现了此求解器方法。我们使用一组可以将其与其他方法进行比较的标准测试容器来证明该方案的鲁棒性。
We present a compatible finite element discretisation for the vertical slice compressible Euler equations, at next-to-lowest order (i.e., the pressure space is bilinear discontinuous functions). The equations are numerically integrated in time using a fully implicit timestepping scheme which is solved using monolithic GMRES preconditioned by a linesmoother. The linesmoother only involves local operations and is thus suitable for domain decomposition in parallel. It allows for arbitrarily large timesteps but with iteration counts scaling linearly with Courant number in the limit of large Courant number. This solver approach is implemented using Firedrake, and the additive Schwarz preconditioner framework of PETSc. We demonstrate the robustness of the scheme using a standard set of testcases that may be compared with other approaches.
