High-order bound-preserving finite difference methods for multispecies and multireaction detonations
High-order bound-preserving finite difference methods for multispecies and multireaction detonations
复制标题
多物种和多反应爆炸的高阶保界有限差分法
DOI：
10.1007/s42967-020-00117-y
复制
发表时间：
2021
影响因子：
1.6
通讯作者：
Yang Yang
中科院分区：
文献类型：
--
作者：
Jie Du;Yang Yang
本文将高阶有限差分格式应用于多物质多反应爆轰（MMD）。在MMD中，密度和压力都是正的，化学反应中第i种物质的质量分数在0到1之间，与。由于缺乏极大值原理，以往的保界技术大多不能直接应用。为了保持这些边界，我们将利用保守的时间积分和系统中一致的数值通量，对所有和强制构造保守格式使用保正技术。此外，爆轰是火焰在预混气体中传播的一种极端奇异模式，该模式中含有显著的刚性源。众所周知，对于具有刚性源的双曲方程，数值近似中靠近激波的过渡点可能引发伪激波速度，从而导致错误的激波位置。直观地说，高阶加权基本非振荡（WENO）格式可以抑制不连续点附近的振荡，是空间离散化的良好选择。然而，随着权值的非线性，数值通量不再“一致”，导致非保守的数值格式和保界技术不起作用。数值实验表明，在不需要进一步的数值技术（如亚单元分辨率）的情况下，具有线性权重的保守FD方法比非保守WENO方案能产生更好的数值逼近。
In this paper, we apply high-order finite difference (FD) schemes for multispecies and multireaction detonations (MMD). In MMD, the density and pressure are positive and the mass fraction of theith species in the chemical reaction, say, is between 0 and 1, with. Due to the lack of maximum-principle, most of the previous bound-preserving technique cannot be applied directly. To preserve those bounds, we will use the positivity-preserving technique to all theand enforceby constructing conservative schemes, thanks to conservative time integrations and consistent numerical fluxes in the system. Moreover, detonation is an extreme singular mode of flame propagation in premixed gas, and the model contains a significant stiff source. It is well known that for hyperbolic equations with stiff source, the transition points in the numerical approximations near the shocks may trigger spurious shock speed, leading to wrong shock position. Intuitively, the high-order weighted essentially non-oscillatory (WENO) scheme, which can suppress oscillations near the discontinuities, would be a good choice for spatial discretization. However, with the nonlinear weights, the numerical fluxes are no longer “consistent”, leading to nonconservative numerical schemes and the bound-preserving technique does not work. Numerical experiments demonstrate that, without further numerical techniques such as subcell resolutions, the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.