论文标题
平衡均衡的高阶有限差异方法
Well-balanced high-order finite difference methods for systems of balance laws
论文作者
论文摘要
在本文中，提出了高阶平衡有限差的加权基本上是非振荡的方法来解决一般的平衡法系统。引入了两个不同的家族：虽然第一个中的方法保留了每个固定解决方案，但第二个家庭中的方法仅保留一组依赖某些参数的固定解决方案。讨论了该方法的准确性，平衡性和保护性能，以及它们在具有奇异源项的系统中的应用。该策略适用于线性标量平衡定律的第三和第五阶良好平衡方法，具有非线性源术语的汉堡方程以及浅水模型。特别是，为后者得出了保留每种固定溶液或仅在静止平衡处的水的数值方法。
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.
