论文标题
任意高级WENO有限体积方案，具有全球化，用于移动平衡保护
Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation
论文作者
论文摘要
在保存固定状态的背景下，例如Cheng等人引入了休息和移动平衡，浅水系统的新配方称为通量全球化。 （2019）。这种方法包括在全球通量中包括源术语的整体，并重建新的全局通量而不是保守变量。最终的方案能够保留一个庞大的平稳且不连续的稳态运动平衡的家庭。在这项工作中，我们专注于全球通量方法的任意高级WENO有限体积（FV）概括。该算法的最精致方面是源通量的适当定义（源项的组成部分）和用于将其与双曲线通量重建相匹配的正交策略。当正确完成此构建后，可以证明由此产生的WENO FV方案承认以恒定全局通量为特征的精确离散稳态。我们还表明，通过针对来源的适当正交策略，我们可以精确地嵌入一些特定的稳态状态，例如休息的湖泊，用于浅水方程。可以表明，全局通量的精确近似可导致具有更好收敛属性和改进溶液的方案。在经典案例中已经测试和验证了新方法：亚临界，超临界和跨临界流。
In the context of preserving stationary states, e.g. lake at rest and moving equilibria, a new formulation of the shallow water system, called Flux Globalization has been introduced by Cheng et al. (2019). This approach consists in including the integral of the source term in the global flux and reconstructing the new global flux rather than the conservative variables. The resulting scheme is able to preserve a large family of smooth and discontinuous steady state moving equilibria. In this work, we focus on an arbitrary high order WENO Finite Volume (FV) generalization of the global flux approach. The most delicate aspect of the algorithm is the appropriate definition of the source flux (integral of the source term) and the quadrature strategy used to match it with the WENO reconstruction of the hyperbolic flux. When this construction is correctly done, one can show that the resulting WENO FV scheme admits exact discrete steady states characterized by constant global fluxes. We also show that, by an appropriate quadrature strategy for the source, we can embed exactly some particular steady states, e.g. the lake at rest for the shallow water equations. It can be shown that an exact approximation of global fluxes leads to a scheme with better convergence properties and improved solutions. The novel method has been tested and validated on classical cases: subcritical, supercritical and transcritical flows.
