论文标题
用于对流问题的数值方案的无限时间解决方案
Infinite Time Solutions of Numerical Schemes for Advection Problems
论文作者
论文摘要
本文解决了一个问题，是否有用于恒定的对流问题的数值方案，可以在无限的时间范围内产生收敛溶液。动机是，在更复杂的对流主导的问题中，这种方法可以作为长期准确解决方案的构建基础。在数值方法的无限时间限制中建立了新的收敛概念之后，我们首先表明线性方法无法满足此收敛标准。然后，我们基于非线性喷射方案框架提出了一种新的数值方法。我们表明，这些方法确实满足了新的收敛标准，因此确定存在在无限时间范围内收敛的数值方法，并证明了该特性产生的长期准确度获得。
This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building blocks for long-time accurate solutions in more complex advection-dominated problems. After establishing a new notion of convergence in an infinite time limit of numerical methods, we first show that linear methods cannot meet this convergence criterion. Then we present a new numerical methodology, based on a nonlinear jet scheme framework. We show that these methods do satisfy the new convergence criterion, thus establishing that numerical methods exist that converge on an infinite time horizon, and demonstrate the long-time accuracy gains incurred by this property.
