The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we introduce nonlinear solver strategies to more robustly and efficiently compute high-speed viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric into the nonlinear least-squares solver that inhibits grid motion in directions with small element length scales. Furthermore, we develop an adaptive elementwise regularization strategy that locally scales the regularization terms as needed to maintain grid validity. We apply the proposed MDG-ICE formulation to test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.

翻译：移动间断伽辽金方法结合界面条件强制（MDG-ICE）是一种高阶r自适应方法，将网格视为变量并弱形式强制执行守恒律、本构律及相应界面条件，从而隐式拟合高梯度流动特征。本文引入非线性求解器策略，以更鲁棒且高效地计算高速粘性流动。具体而言，我们将基于网格隐含度量的各向异性网格正则化纳入非线性最小二乘求解器中，抑制单元尺度较小方向上的网格运动。此外，我们开发了一种自适应单元级正则化策略，按需局部缩放正则化项以维持网格有效性。我们将所提出的MDG-ICE公式应用于涉及粘性激波和/或边界层的测试案例，包括马赫数17.6的圆柱绕流和马赫数5的球体绕流，这些对于传统数值格式在单纯形网格上的计算极具挑战性。即使不引入人工耗散，计算解也不会出现伪振荡，并生成高度对称的表面热流分布。