论文标题
代数熵修复和凸限制标量双曲线保护法的连续有限元离散法
Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
论文作者
论文摘要
在这项工作中，我们使用新的代数校正程序修改标量双曲保护法的连续盖尔金离散化。离散的熵条件用于确定熵稳定的最小量，并限制对财产保存的低阶方案的纠正。在近乎熵的保守数值通量的抗原部分中添加二阶熵耗散成分通常不足以防止冲击区域中侵犯局部界限。我们的整体凸限制技术以保证不变域，局部最大原理的有效性和熵稳定性的方式调整给定目标通量。新方法结合了现代熵稳定/熵保守计划的优势及其当地的极值减少。代数通量校正的过程基于不平等约束，该约束可证明提供所需的属性。不涉及免费参数。所提出的代数修复很容易适用于非结构化网格，有限元方法，一般时间离散和稳态残差。对线性和非线性测试问题进行了显式熵约束方案的数值研究。
In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization and constrain antidiffusive corrections of a property-preserving low-order scheme. The addition of a second-order entropy dissipative component to the antidiffusive part of a nearly entropy conservative numerical flux is generally insufficient to prevent violations of local bounds in shock regions. Our monolithic convex limiting technique adjusts a given target flux in a manner which guarantees preservation of invariant domains, validity of local maximum principles, and entropy stability. The new methodology combines the advantages of modern entropy stable/entropy conservative schemes and their local extremum diminishing counterparts. The process of algebraic flux correction is based on inequality constraints which provably provide the desired properties. No free parameters are involved. The proposed algebraic fixes are readily applicable to unstructured meshes, finite element methods, general time discretizations, and steady-state residuals. Numerical studies of explicit entropy-constrained schemes are performed for linear and nonlinear test problems.
