In this paper, we propose a new class of second-order one-step time-splitting schemes for scalar and systems of conservation laws. The strategy is based on a relaxation approximation which consists in introducing a relaxation system with linearly degenerate characteristic fields to approximate the original system and deal with its nonlinearities. The numerical schemes are based on the use of arbitrarily high-order approximations of the underlying linear advection equations. Numerical evidence is proposed to illustrate the behaviour of our schemes.

中文翻译：

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基于标量松弛系统和守恒定律系统的二阶方案


在本文中，我们为标量和守恒定律系统提出了一类新的二阶一步时间分割方案。该策略基于弛豫近似，包括引入具有线性简并特征场的弛豫系统来近似原始系统并处理其非线性。数值方案基于对底层线性平流方程的任意高阶近似。提出了数字证据来说明我们的方案的行为。