论文标题
一种基于隐式泰勒系列扩展的通用高阶方法，其空间衍生物的快速二阶演化
A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives
论文作者
论文摘要
在本文中，提出了一种用于解决双曲平衡定律的中心通用高级有限体积方法。该计划属于Ader方法家族，其中广义的Riemann问题（GRP）是一个基础。解决这些问题的解决方案是通过隐式泰勒系列扩展进行的，该系列使该方案可以很好地适用于僵硬的源术语。进行了von Neumann稳定性分析，以研究稳定性和准确性平衡的CFL值范围。该方案实现了一种居中的低消散方法，用于处理从小型CFL值中获利的系统的对流部分。数值测试表明，当前的方案也可以在保守和非保守形式中有效地解决双曲平衡定律。经验收敛率评估表明，预期的理论准确度达到了第五阶。
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The solution to these problems is carried through an implicit Taylor series expansion, which allows the scheme to works very well for stiff source terms. A von Neumann stability analysis is carried out to investigate the range of CFL values for which stability and accuracy are balanced. The scheme implements a centred, low dissipation approach for dealing with the advective part of the system which profits from small CFL values. Numerical tests demonstrate that the present scheme can solve, efficiently, hyperbolic balance laws in both conservative and non-conservative form as well. An empirical convergence rate assessment shows that the expected theoretical orders of accuracy are achieved up to the fifth order.
