Iterative process acceleration of calculation of unsteady, viscous, compressible, and heat-conductive gas flows

作者：Shterev K S^*

来源：International Journal for Numerical Methods in Fluids, 2015, 77(2): 108-122.

DOI：10.1002/fld.3979

• initial guess extrapolation
• Lagrange polynomial extrapolation
• Navier-Stokes-Fourier equations
• gas microflows

In this paper, extrapolation technique is introduced in the Semi-Implicit Method for Pressure-Linked Equations - Time Step (SIMPLE-TS) finite volume iterative algorithm for calculation of compressible Navier-Stokes-Fourier equations subject of slip and jump boundary conditions. The initial state, required by the iterative solver in simulation of unsteady flow problems, is approximated in time by Lagrange polynomial extrapolation in each node. The approach is applicable to a parallel code in a straightforward way due to algorithmic independence of the neighboring nodes in the computational grid. A criterion is proposed to determine the order of extrapolation polynomial and stop the extrapolation execution, when the local steady state is reached. The approach is tested on different microflow problems: Couette flow, flow past a square in a microchannel at subsonic and supersonic speeds, and convective Rayleigh-Benard flow of a rarefied gas. The acceleration varies from 1.14-fold to 2.8-fold.

• 出版日期2015-1-20