论文标题
高分辨率紧凑的隐式数值计划
High resolution compact implicit numerical scheme for conservation laws
论文作者
论文摘要
我们为时间依赖性保护定律的数值解决方案提供了一种新颖的隐式方案。提出的方法的核心思想是利用和近似溶液中混合的时空衍生物，在及时得出某些二阶精确方案时自然发生。当使用PDE的空间导数完全替换，但保留了混合衍生物，则在Lax-Wendroff（或Cauchy-Kowalevski）过程的背景下引入这种方法。如果以合适的方式近似，则由此产生的紧凑隐式方案产生的代数系统比完全隐式方案得出的系统具有更方便的结构。在一维情况下，我们为某些代表性双曲方程（包括说明性的数值实验）提供了隐式方案的高分辨率TVD形式。
We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea of the presented method is to exploit and approximate the mixed spatial-temporal derivative of the solution that occurs naturally when deriving some second order accurate schemes in time. Such an approach is introduced in the context of the Lax-Wendroff (or Cauchy-Kowalevski) procedure when the second time derivative is not completely replaced by space derivatives using the PDE, but the mixed derivative is kept. If approximated in a suitable way, the resulting compact implicit scheme produces algebraic systems that have a more convenient structure than the systems derived by fully implicit schemes. We derive a high resolution TVD form of the implicit scheme for some representative hyperbolic equations in the one-dimensional case, including illustrative numerical experiments.
