论文标题
通过使用线性编程，通过通量校正的标量双曲线保护法和对流扩散方程
Flux-corrected transport for scalar hyperbolic conservation laws and convection-diffusion equations by using linear programming
论文作者
论文摘要
通量校正的运输（FCT）是通量限制器方法之一。与总变化减少方法不同，获得用于计算通量限制器的已知FCT公式并不十分透明，当原始差分运算符变化时，它们的转换并不明显。我们提出了一种新型的形式数学方法，以使用线性编程来设计加权混合差异方案的通量校正。混合方案是单调方案和高阶方案的线性组合。最大抗原通量的确定被视为线性目标函数的优化问题。为了获得优化问题的约束，对单调差异方案有效的不平等应用应用于混合差异方案。非线性优化问题的数值解决方案降低为线性编程问题的迭代解决方案。相应的线性编程问题的非平凡近似解决方案可以视为所需的通量限制器。我们提供标量双曲线保护法和对流扩散方程的通量校正公式。设计的通量校正的标量双曲线保护定律产生熵解决方案。提出了数值结果。
Flux-corrected transport (FCT) is one of the flux limiter methods. Unlike the total variation diminishing methods, obtaining the known FCT formulas for computing flux limiters is not quite transparent, and their transformation is not obvious when the original differential operator changes. We propose a novel formal mathematical approach to design flux correction for weighted hybrid difference schemes by using linear programming. The hybrid scheme is a linear combination of a monotone scheme and a high order scheme. The determination of maximal antidiffusive fluxes is treated as an optimization problem with a linear objective function. To obtain constraints for the optimization problem, inequalities that are valid for the monotone difference scheme are applied to the hybrid difference scheme. The numerical solution of the nonlinear optimization problem is reduced to the iterative solution of linear programming problems. A nontrivial approximate solution of the corresponding linear programming problem can be treated as the required flux limiters. We present flux correction formulas for scalar hyperbolic conservation laws and convection-diffusion equations. The designed flux-corrected transport for scalar hyperbolic conservation laws yields entropy solutions. Numerical results are presented.
