A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

Gas-kinetic schemes for unsteady compressible flow simulations

The present investigation is aimed at evaluating the reliability of the unstructured TAU Code for hypersonic flows. To improve the efficiency, accuracy and robustness, the code has been modified concerning, for example, residual smoothing, limiters and timestep size to handle strong shocks. Validation was done using CFD solutions of different European CFD solvers for well known test cases such as hyperboloid flare. Further investigations have been done for wedge compression corners to study gap flow phenomena. Also, computations for a complex three dimensional configuration including deflected body flaps while considering the gap effect on the thermal loads have been performed. The effect of 3d adaptation has been intensively studied. The present investigation shows that the TAU-code is a reliable and efficient tool for complex cold hypersonic flow solutions, although its performance with respect to computing time should be improved.

Validation of the Unstructured DLR-TAU-Code for Hypersonic Flows

Kinetic Flux-Vector Splitting for the Navier-Stokes Equations

The equilibrium flux method for the calculation of flows with non-equilibrium chemical reactions

https://espace.library.uq.edu.au/view/UQ:135115/JMS_abdel-jawad_etal_april07_v8_revised.pdf

Flowfields on feed and permeate sides of tubular molecular sieving silica (MSS) membranes

Flowfields on Feed and Permeate Sides of Tubular Molecular Sieving Silica

A particle simulation method, the “relaxation time” simulation method (RTSM), is described. In RTSM the collision phase in standard DSMC is replaced by a procedure whereby some of the particle velocities in each cell at each time step are selected from an equilibrium distribution, while conserving the total energy and momentum in the cell. The remaining velocities in each cell are not changed. The number of velocities to be changed is determined from the local relaxation time, which can be derived from the cell density and temperature and any desired viscosity law. The relaxation time method is a simulation method to solve the BGK equation. RTSM is efficient compared to DSMC, and becomes more so as the collision rate increases, so RTSM appears to be a natural candidate for near continuum flows.

/pdf/a-particle-simulation-method-for-the-bgk-equation-29kk1nc2wf.pdf

Michael N. Macrossan

Papers

The equilibrium flux method for the calculation of flows with non-equilibrium chemical reactions

Flowfields on feed and permeate sides of tubular molecular sieving silica (MSS) membranes

Flowfields on Feed and Permeate Sides of Tubular Molecular Sieving Silica

A particle simulation method for the BGK equation

v -DSMV: a fast simulation method for rarefield flow