重新审视特征方法 via 凸包算法
Revisiting the method of characteristics via a convex hull algorithm
AI总结：
本文提出凸包算法用于计算非线性对流守恒律的熵耗散和熵守恒解，适用于凸或非凸通量问题，并通过数值实验验证其有效性。
摘要：
我们重新审视特征方法用于非线性超几何问题的激波波解，并描述一种新的数值算法——凸包算法（CHA），以计算熵耗散解（满足所有相关熵不等式）和熵守恒（或多值）解。我们的方法也适用于哈密尔顿-雅可比方程及其他具有特征方法的问题。从特征方法确定的多值解中，我们的算法“提取”熵耗散解，即使在激波形成后也能应用。它适用于凸或非凸通量/哈密尔顿量。我们通过各种数值实验，包括流体动力学问题，证明了所提出方法的相关性。
英文摘要：
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - in order to compute, both, entropy dissipative solutions (satisfying all relevant entropy inequalities) and entropy conservative (or multivalued) solutions to nonlinear hyperbolic conservation laws. Our method also applies to Hamilton-Jacobi equations and other problems endowed with a method of characteristics. From the multivalued solutions determined by the method of characteristic, our algorithm "extracts" the entropy dissipative solutions, even after the formation of shocks. It applies to, both, convex or non-convex flux/Hamiltonians. We demonstrate the relevance of the proposed approach with a variety of numerical tests including a problem from fluid dynamics.
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