Synchronized slope limiting in discontinuous Galerkin methods for the equations of gas dynamics
Synchronized slope limiting in discontinuous Galerkin methods for the equations of gas dynamics
复制标题
气体动力学方程不连续伽辽金方法的同步斜率限制
DOI：
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复制
发表时间：
2016
期刊：
影响因子：
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通讯作者：
C. Lohmann
中科院分区：
文献类型：
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作者：
D. Kuzmin;C. Lohmann
本文提出了一种新的方法，用于在不连续的Galerkin（DG）方法中同步限制密度，能量和压力跳跃的方法。标量数量的Barth-Jespersen限制器的基于顶点的版本被推广，以限制保守变量的梯度，以确保所有关注数量保留在可允许的值范围内。相应的不平等约束的界限旨在在强密度变化区域内强制执行局部最大原则，并且在平滑区域的限制较少。提出的限制策略保证了阳性保存，并导致同步梯度校正因子的封闭形式表达式，而无需解决不平等约束的优化问题。对于二维测试问题进行了数值研究。
This paper presents a new approach to synchronized limiting of density, energy, and pressure jumps in discontinuous Galerkin (DG) methods for the Euler equations of gas dynamics. A vertex-based version of the Barth-Jespersen limiter for scalar quantities is generalized to constrain the gradients of the conservative variables in a way which guarantees that all quantities of interest remain in the range of admissible values. The bounds for the corresponding inequality constraints are designed to enforce local maximum principles in regions of strong density variations and become less restrictive in smooth regions. The proposed limiting strategy guarantees positivity preservation and leads to closed-form expressions for the synchronized gradient correction factors without the need to solve inequality-constrained optimization problems. A numerical study is performed for two-dimensional test problems.
具有局部限制器的嵌入式不连续伽辽金输运方案
DOI：
10.1016/j.jcp.2016.02.021
发表时间：
2016
期刊：
J. Comput. Phys.
影响因子：
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作者：
C.J. Cotter;D. Kuzmin
通讯作者：
D. Kuzmin