H3PC: Hypersonic, High-Order, High-Performance Code with Adaptive Mesh Refinement and Real Chemistry

TL;DR

The paper presents H$^3$PC, a high-order, high-performance hypersonic solver built on the Trixi.jl DG framework, extended with adaptive mesh refinement, entropy-stable fluxes, a parabolic solver for viscous terms on a P4est mesh, and real chemistry via Mutation++. It demonstrates accurate, scalable simulations of subsonic to hypersonic flows with non-equilibrium chemistry, validated against Taylor–Green vortex benchmarks, circular and square cylinder flows, and a P8-inlet, and shows competitive performance and stability on CPU-based exascale-like parallelism. Key contributions include the integration of Mutation++ through Julia’s FFI, the development of a parallel parabolic solver, and AMR-enabled high-order simulations of complex thermo-chemical hypersonic flows, with cross-validation against UCNS3D. The framework enables robust prediction of shocks, turbulence, and chemical kinetics in complex geometries, with potential extensions to multi-GPU platforms and ionization/plasma modeling.

Abstract

We have developed a hypersonic high-order, high-performance code (H$^3$PC) utilizing the ``Trixi.jl" framework in order to simulate both non-reactive and chemically reactive compressible Euler and Navier-Stokes equations for complex three-dimensional geometries. H$^3$PC is parallel on CPU platforms and can perform exascale parallel computations of hypersonic turbulent flows. The numerical approach is based on the discontinuous Galerkin spectral element method, satisfying the entropy and energy stability conditions for the Euler equations. H$^3$PC can perform simulations of high-speed flows from subsonic to hypersonic speeds based on frozen, equilibrium, and non-equilibrium chemistry modeling of the gas mixture, using the \texttt{Mutation.jl} , which is a Julia package developed to wrap the C++-based Mutation++ library. H$^3$PC can also perform parallel adaptive mesh refinement for two- and three-dimensional Euler and Navier-Stokes discretizations with non-conforming elements. In this study, we first demonstrate the successful integration of Mutation++ into the H$^3$PC solver, and then verify its accuracy through simulations of Taylor-Green vortex flow, supersonic flow past a square and circular cylinder, and hypersonic P8-inlet.

Figures (24)

• Figure 1: Schematic of Hypersonic-Euler equations type for H$^3$PC solver.
• Figure 2: Hypersonic blast wave, (a) Density of $N$, (b) Density of $O$, (c) Density of $NO$, (d) Density of $N_2$, (e) Density of $O_2$ (f) Temperature, (g) Velocity magnitude. The domain is discretized by employing $64\times64$ elements with $\mathcal{P}=3$. The flow is initialized using the modified Sod problem by Grossman grossman1990flux. A high temperature region is imposed inside a circle with radius of 0.5 at the center of the square domain with $x,y \in [-1,1]^2$.
• Figure 3: Comparison of element size and polynomial order for the non-equilibrium blast wave problem.
• Figure 4: Taylor-Green Vortex for $M=0.1$ and $Re=1600$. shown are the spatial dissipation and kinetic energy time evolution. For the $\textrm{H}^3\textrm{PC}$, $\mathcal{P}=7$ and the number of elements for each Cartesian direction is set as 11, 16, and 24. For the UCNS3D solver, we have employed 22, 32, and 48 with accuracy order of 4.
• Figure 5: Taylor-Green Vortex contour plots for $M=0.1$ and $Re=1600$. (a) Adaptive mesh refinement based on velocity magnitude indicator, (b) Velocity magnitude contours for $t=9.13$, (c) Iso-surfaces of Q-criterion=0.01 colored by the velocity magnitude. The color range for the velocity magnitude ranges from dark blue at 2.3e-4 to dark red at $1.2$.