Computational simulations of near-continuum gas flow using Navier-Stokes-Fourier equations with slip and jump conditions based on the modal discontinuous Galerkin method

Abstract

Blunt-body configurations are the most common geometries adopted for non-lifting re-entry vehicles. Hypersonic re-entry vehicles experience different flow regimes during flight due to drastic changes in atmospheric density. The conventional Navier-Stokes-Fourier equations with no-slip and no-jump boundary conditions may not provide accurate information regarding the aerothermodynamic properties of blunt-bodies in flow regimes away from the continuum. In addition, direct simulation Monte Carlo method requires significant computational resources to analyze the near-continuum flow regime. To overcome these shortcomings, the Navier-Stokes-Fourier equations with slip and jump conditions were numerically solved. A mixed-type modal discontinuous Galerkin method was employed to achieve the appropriate numerical accuracy. The computational simulations were conducted for different blunt-body configurations with varying freestream Mach and Knudsen numbers. The results show that the drag coefficient decreases with an increased Mach number, while the heat flux coefficient increases. On the other hand, both the drag and heat flux coefficients increase with a larger Knudsen number. Moreover, for an Apollo-like blunt-body configuration, as the flow enters into non-continuum regimes, there are considerable losses in the lift-to-drag ratio and stability.

Behavior of a shock-accelerated heavy cylindrical bubble under nonequilibrium conditions of diatomic and polyatomic gases

“…Over recent decades, the discontinuous Galerkin (DG) method is gaining widespread popularity as an alternative approach to solving partial differential equations. The DG method combines the main features associated with the finite element and finite volume methods and have been successfully applied to a wide range of applications in gas dynamics, acoustics waves, plasma physics, quantum physics, and magnetohydrodynamics [45][46][47][48][49][50][51][52]. The DG method has numerous important features, including hp adaptivity; robustness with strong mathematical properties, well defined for structured/unstructured meshes associated within complex geometries; well suited for nonconforming elements having hanging nodes; very efficient for adopting time-stepping algorithms and highly parallelizable.…”

Contribution of Mach number to the evolution of the Richtmyer-Meshkov instability induced by a shock-accelerated square light bubble

“…Discontinuous Galerkin (DG) approaches have recently gained prominence in fields ranging from fluid mechanics to acoustics, biological process, and electromagnetics [42,43,[55][56][57][58][59][60][61][62][63][64][65][66]. These methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements.…”

Contribution of Mach number on the evolution of Richtmyer-Meshkov instability induced by shock-accelerated square light bubble

“…Discontinuous Galerkin (DG) approaches have recently gained prominence in fields ranging from fluid mechanics to acoustics and electromagnetics [44,45,[56][57][58][59][60][61][62][63][64][65][66]. These methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements.…”