论文标题
熵稳定通量校正标量双曲线保护法
Entropy stable flux correction for scalar hyperbolic conservation laws
论文作者
论文摘要
众所周知，通量校正的运输算法可以产生双曲线保护法的熵侵入溶液。我们的目的是使用最大抗原通量设计通量校正，以获得标量双曲线保护定律的熵解决方案。为此，我们考虑了一种混合差异方案，该方案是单调方案和高阶精度方案的线性组合。混合方案的通量限制器是根据相应的优化问题计算得出的。优化问题的约束包括对单调方案有效并应用于混合方案的不平等。我们将离散的细胞熵不等式与适当的数值熵通量应用于标量双曲线保护法的物理相关解决方案。优化问题的非平凡近似解会产生表达式以计算所需的通量限制器。我们提出的例子表明，并非所有的数值熵通量都可以保证单一正确正确的标量双曲线保护定律解决方案。
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar hyperbolic conservation laws. To do this we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a scheme of high-order accuracy. Flux limiters for the hybrid scheme are calculated from a corresponding optimization problem. Constraints for the optimization problem consist of inequalities that are valid for the monotone scheme and applied to the hybrid scheme. We apply the discrete cell entropy inequality with the proper numerical entropy flux to single out a physically relevant solution of scalar hyperbolic conservation laws. A nontrivial approximate solution of the optimization problem yields expressions to compute the required flux limiters. We present examples that show that not all numerical entropy fluxes guarantee to single out a physically correct solution of scalar hyperbolic conservation laws.
