Development of high-order discontinuous Galerkin methods for simulations of high-speed particle-laden fluid flows
Keywords: Mechanical Engineering.

An encouraging alternative to conventional finite-volume and finite-difference schemes for computational fluid dynamics is the discontinuous Galerkin (DG) method. This method combines aspects of finite-element and finite-volume schemes, employing piecewise polynomials to approximate the solution. It offers a number of advantages, such as arbitrarily high order of accuracy with a compact stencil on unstructured meshes. Furthermore, it is well-suited for advanced mesh adaptation strategies and can achieve great efficiency on graphics processing units (GPUs). However, there are several challenges as well. One of these is the robust capturing of shocks and other flow-field discontinuities. In addition, compared to more mature numerical methods, the DG scheme lacks a well-established infrastructure for handling complex physics, such as particle-laden flows. In light of this, the overarching objective of this work is to develop a DG framework for simulating high-speed particle-laden fluid flows and then apply the resulting methodology to investigate hypersonic dusty flows over blunt bodies, with special focus on Mars atmospheric entry. A simple and robust shock capturing method is first developed. The method employs intra-element variations for shock detection and smooth artificial viscosity for stabilization. We apply the shock capturing method to compute canonical hypersonic test cases, such as flows over a cylinder and a double cone. Quantitative comparisons with state-of-the-art finite-volume codes demonstrate significant benefits of the proposed DG formulation for hypersonic flow computations. In particular, in contrast with finite-volume techniques, the DG method can accurately predict surface heating with strong mesh-shock alignment and with fewer degrees of freedom. We then develop a methodology for simulating particle-laden flows with the DG scheme. The particles are described in a Lagrangian manner. The use of curved elements, which are necessary in high-order DG simulations involving curved geometries, presents significant challenges for tracking and localizing the particles on the Eulerian mesh. We propose strategies to handle particle-wall collisions on arbitrary curved, high-aspect-ratio elements, and we find that curved elements can significantly improve predictions of particle trajectories. In addition, an algorithm is developed for treating interparticle collisions that exploits the geometric mapping from physical space to reference space. The algorithm can significantly reduce computational cost compared to conventional strategies. We also develop smooth anisotropic kernels for projecting the effect of the particle phase onto the Eulerian mesh in a robust, accurate, and efficient manner, particularly on high-aspect-ratio elements. Simulations of shock-particle interaction, sandblasting, and other applications illustrate the ability of the developed algorithms to effectively compute complex multiphase flows. Finally, we apply the resulting Euler-Lagrange methodology to compute hypersonic dusty flows over blunt bodies. To address the overall lack of high-quality experimental data, a parametric study is conducted to investigate the sensitivities of the solution to the physical modeling of the particle phase. We also simulate dusty flows over the full-scale ExoMars Schiaparelli capsule at realistic flow conditions. Detailed analysis of particle trajectories through the shock layer is performed. The effects of the dust particles on heat shields, such as heat flux augmentation and surface recession, are characterized