平衡律方程组的平衡高阶有限差分法
Well-balanced high-order finite difference methods for systems of balance laws
摘要：
本文提出了求解一般平衡律组的高阶平衡加权本质不振荡有限差分方法。引入了两个不同的家庭：而在第一个保持每一个固定的解决方案，在第二个家庭的方法只保留一个给定的一组固定的解决方案，取决于一些参数。的准确性，良好的平衡性，和守恒性质的方法进行了讨论，以及它们的应用系统与奇异源项。该策略被应用到推导三阶和五阶的线性标量平衡法，Burgers方程与非线性源项，浅水模式的良好平衡的方法。特别是，数值方法，保持每一个固定的解决方案，或只有水在休息平衡，后者。
英文摘要：
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one preserve every stationary solution, those in the second family only preserve a given set of stationary solutions that depend on some parameters. The accuracy, well-balancedness, and conservation properties of the methods are discussed, as well as their application to systems with singular source terms. The strategy is applied to derive third and fifth order well-balanced methods for a linear scalar balance law, Burgers' equation with a nonlinear source term, and for the shallow water model. In particular, numerical methods that preserve every stationary solution or only water at rest equilibria are derived for the latter.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
