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Numerical Heat Transfer And Fluid Flow

Kinetic theory and irreversible thermodynamics

Shock-accelerated bubbles have long been an intriguing topic for understanding the fundamental physics of turbulence generation and mixing caused by the Richtmyer–Meshkov instability. In this study, the impact of bulk viscosity on the flow morphology of a shock-accelerated cylindrical light bubble in diatomic and polyatomic gases is investigated numerically. An explicit mixed-type modal discontinuous Galerkin scheme with uniform meshes is employed to solve a two-dimensional system of unsteady physical conservation laws derived rigorously from the Boltzmann–Curtiss kinetic equations. We also derive a new complete viscous compressible vorticity transport equation including the bulk viscosity. The numerical results show that, during the interaction between a planar shock wave and a cylindrical light bubble, the bulk viscosity associated with the viscous excess normal stress in diatomic and polyatomic gases plays an important role. The diatomic and polyatomic gases cause significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. In contrast to monatomic gases, diatomic and polyatomic gases produce larger rolled-up vortex chains, various inward jet formations, and large mixing zones with strong, large-scale expansion. The effects of diatomic and polyatomic gases are explored in detail through phenomena such as the vorticity generation, degree of nonequilibrium, enstrophy, and dissipation rate. Furthermore, the evolution of the shock trajectories and interface features is investigated. Finally, the effects of bulk viscosity on the flow physics of shock-accelerated cylindrical light bubble are comprehensively analyzed.

Impact of bulk viscosity on flow morphology of shock-accelerated cylindrical light bubble in diatomic and polyatomic gases

In this study, we present simulations of strongly out-of-equilibrium conditions for the one-dimensional electron Boltzmann transport equation (BTE) in semiconductor devices. An explicit modal discontinuous Galerkin method is employed to solve the electron BTE along with the simplest collisional model–relaxation time approximation. The electron BTE system is discretized in momentum and time, and applied to the description of the dynamics of non-linear electron transport under a strong static electric field. A third-order explicit SSP-RK scheme is adopted for the temporal discretization of the resulting semi-discrete ODE. For the steady-state electron BTE, the analytical solutions are derived at low and high electric fields which are used to validate the numerical approach. The computed solution show a good agreement with derived analytic solution in wide range of tested parameters and regimes. An extensive range of numerical simulations has also been performed to investigate the impact of exploited flow parameters on the electron BTE solutions. Ultimately, these results predict that the modal DG approach is particularly effective in treating the strongly out-of-equilibrium regimes encountered like in ultrafast transport dynamics.

Strongly Out-of-Equilibrium Simulations for Electron Boltzmann Transport Equation Using Modal Discontinuous Galerkin Approach

An explicit modal discontinuous Galerkin method for Boltzmann transport equation under electronic nonequilibrium conditions

A three-dimensional modal discontinuous Galerkin method for the second-order Boltzmann-Curtiss-based constitutive model of rarefied and microscale gas flows

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.

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

Thermal and flow characteristics of nonequilibrium monatomic, diatomic, and polyatomic gases in cylindrical Couette flow based on second-order non-Navier–Fourier constitutive model

T. Chourushi

Papers

A three-dimensional modal discontinuous Galerkin method for the second-order Boltzmann-Curtiss-based constitutive model of rarefied and microscale gas flows

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

Thermal and flow characteristics of nonequilibrium monatomic, diatomic, and polyatomic gases in cylindrical Couette flow based on second-order non-Navier–Fourier constitutive model

A High Resolution Equi-Gradient scheme for convective flows

Proposition of modified convection boundedness criterion and its evaluation for the development of bounded schemes