A moving-grid, shock-fitting, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler or Navier-Stokes equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. The method is implemented in two-dimensions in the context of a streamwise upwind Petrov-Galerkin finite element discretization with unstructured triangular meshes and mesh adaptation. It is shown that the shock interface motion equation has a wave nature, and disturbances can propagate along the shock interface. A SUPG stabilization term is introduced to the interface motion equation that is critical for ensuring that interface disturbances do not lead to non-convergent solution behavior. The formal order of accuracy of the scheme is verified, and the performance of the proposed scheme is assessed for both inviscid and viscous problems. It was found that the present scheme predicts smooth and noise-free surface heating for hypersonic flow over a cylinder with purely irregular triangular elements.

已经实现了一种移动网格，减震拟合的有限元方法，该方法可以对带有冲击的流动模拟实现高阶精度。在这种方法中，将计算网格中的元素边缘拟合到冲击前沿，并在整个模拟过程中与冲击一起移动。在任意Lagrangian-Eulerian框架中的运动网格上求解Euler或Navier-Stokes方程。该方法是在具有非结构化三角形网格和网格自适应的顺风逆流Petrov-Galerkin有限元离散化的背景下二维实现的。结果表明，激波界面运动方程具有波动性质，扰动可沿激波界面传播。SUPG稳定项被引入到界面运动方程中，这对于确保界面扰动不会导致非收敛解行为至关重要。验证了该方案准确性的形式顺序，并针对无粘性和粘性问题评估了所提出方案的性能。已经发现，本方案预测了具有纯不规则三角形元件的圆柱体上的超音速流的光滑且无噪声的表面加热。