一种时空平滑人工粘性方法与小波噪声指示器和冲击碰撞方案，第二部分：二维情况
A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: the 2-D case
AI总结：
本文提出了一种二维情况下的时空平滑人工粘性方法，结合小波噪声指示器和冲击碰撞方案，用于准确模拟射流-泰勒不稳定性、冲击碰撞和反弹等现象。
摘要：
本文是我们的配套论文[18]的第二部分。在此，我们扩展了在[20,18]中开发的C方法，将其推广到二维空间中，用于在非线性守恒律系统中添加局部的、时空平滑的人工粘性，以传播激波、稀疏波和接触不连续性。对于气体动力学，C方法将欧拉方程与标量反应扩散方程（称为C方程）耦合，其解用作激波和接触的时空平滑人工粘性指示器。我们开发了一种高阶数值算法，用于二维气体动力学，可以准确模拟射流-泰勒（RT）不稳定性、凯尔文-赫姆霍兹（KH）卷起接触不连续性、冲击碰撞和反弹。我们实现了方向上各向同性和各向异性的人工粘性方案，后者仅在演化前沿的切向方向添加扩散。此外，我们还产生了一种新的冲击碰撞指示函数，该函数在冲击碰撞期间自然激活，然后平滑地 deactivate。此外，我们还实现了高频率二维小波基噪声检测器以及高效的局部噪声去除算法。我们为一些经典的二维测试问题提供了数值结果，包括RT问题、Noh问题、Liska和Wendroff[13]综述论文中的圆形爆炸问题、Sedov爆波问题、双马赫10反射测试以及冲击-壁碰撞问题。特别是，我们展示了我们的人工粘性方法可以消除Noh问题中的壁加热现象，从而产生准确的非振荡解，尽管我们的简化WENO型方案无法运行此问题。
英文摘要：
This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-oscillatory solution, even though our simplified WENO-type scheme fails to run for this problem.
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