Advanced Physical Models and Numerical Algorithms to Enable High-Fidelity Aerothermodynamic Simulations of Planetary Entry Vehicles on Emerging Distributed Heterogeneous Computing Architectures

The objective of this research project is the development of innovative physical models and advanced numerical methods for the reliable prediction of aerothermodynamic flows that are relevant to hypersonic and atmospheric entry vehicles. As such, this research addresses limitations of currently employed aerothermodynamic modeling capabilities that largely rely on traditional low-order finite-difference/finite-volume formulations. The algorithmic research effort addresses the critical evaluation of high-order discontinuous Galerkin (DG) methods for simulating aerothermodynamic flows and heat-transfer on unstructured and non-conformal meshes. Fundamental algorithmic research efforts will focus on the development of an adaptation method and a shock-capturing technique that utilize rigorous entropy-residual functions. To achieve optimal performance on emerging heterogeneous and memory-complex compute architectures, the potential of using domain-specific programming paradigms for accelerating high-fidelity aerothermodynamic simulations by performing compute-intensive kernel functions (for chemistry integration and quadrature evaluation) on heterogeneous coprocessors will be evaluated. To enable the accurate simulation of particle-laden reacting flow environments, a Lagrangian particle method will be developed. This method considers the coupling between turbulence, particle dispersion, radiation, pyrolysis, and non-equilibrium chemistry; the evolution of the disperse phase will be coupled with the carrier phase to account for exchange of mass, momentum, energy, devolatilization, and phase transition. Ground-test experiments and flight data will be used to facilitate comprehensive code validation, and code-to-code comparisons with current EDL-simulation capabilities will be performed. An ambitious performance target is to demonstrate efficiency improvements of the resulting high-order DG-method by at least an order of magnitude compared to state-of-the-art aerothermodynamic codes at comparable or even better accuracy and robustness. 
The major contributions of this work are summarized below:
• A shock capturing method for the DG scheme is developed. The method is simple and robust and enables accurate simulations of viscous hypersonic flows with surface heating as a target quantity, which hitherto have been very limited in the context of high-order methods. To our knowledge, the first accurate high-order DG simulation of hypersonic flow over a double cone, or a problem of similar nature and complexity, is performed. We also demonstrate robust computations of viscous hypersonic flows with the thermally perfect gas model, which should increase confidence in the ability of the high-order DG method to simulate hypersonic flows in thermochemical nonequilibrium.
• Quantitative comparisons with LAURA and FUN3D, two of NASA’s state-of-the-art hypersonic flow solvers, are performed. These results demonstrate notable advantages of the DG method over FV techniques. Specifically, high-order DG predictions of surface heating are significantly less sensitive than FV predictions to mesh-shock mis-alignment and the choice of inviscid flux function. In addition, we show that fewer degrees of freedom are needed to achieve mesh convergence in DG simulations than in FV simulations.
• An Euler-Lagrange methodology for computing disperse multiphase flows is developed in a DG framework. Despite some existing work on employing the DG method to simulate particle-laden flows, the proposed methodology significantly extends current capabilities by enabling efficient multiphase flow simulations on arbitrary curved, high-aspect-ratio elements. In particular, the challenges associated with such elements when tracking particles (including particle-wall collisions) and computing the reverse coupling of particles to the carrier gas in a robust and accurate fashion are addressed. A key finding is that a high-order geometric approximation can significantly improve predictions of particle trajectories when particles collide with curved solid boundaries. We also propose an interparticle collision algorithm that can significantly reduce computational cost compared to conventional schemes. We employ the Euler-Lagrange formulation to applications such as shock-particle interaction and sandblasting.
• The developed DG framework (shock capturing and particle methods) is successfully applied to hypersonic dusty flows over blunt bodies. Good agreement with experimental data is obtained. To address the fact that additional high-quality experiments are still required for further critical validation, sensitivities of the predicted solution to the physical modeling of the particle phase are assessed. We also perform high-fidelity simulations of hypersonic dusty flow over the full-scale Schiaparelli capsule at realistic conditions to improve understanding of the relevant physics. Dust-induced surface recession and heating augmentation are parametrically studied.