论文标题
熵矩阵的有效计算熵稳定的逐件总和计划
Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes
论文作者
论文摘要
熵稳定方案在半污垢水平上复制熵不等式。这些方案依赖于逐个代数总和（SBP）结构和一种称为通量差异的技术。我们为Jacobian矩阵提供了简单有效的公式，用于熵稳定离散化产生的ODE的半混凝土系统。这些公式是根据通量差异和通量函数的衍生物的结构得出的，可以使用自动分化（AD）计算。数值结果证明了这些Jacobian公式的效率和实用性，然后在两衍生明确的时间步长方案和隐式时间稳定的情况下使用。
Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient formulas for Jacobian matrices for the semi-discrete systems of ODEs produced by entropy stable discretizations. These formulas are derived based on the structure of flux differencing and derivatives of flux functions, which can be computed using automatic differentiation (AD). Numerical results demonstrate the efficiency and utility of these Jacobian formulas, which are then used in the context of two-derivative explicit time-stepping schemes and implicit time-stepping.
