High-order compact exponential finite difference methods for convection–diffusion type problems

Performance of geometric multigrid method for coupled two-dimensional systems in CFD

“…The results obtained as to the number of levels in the Laplace equation are consistent with existing literature: [34] recommended the use of L = L max ; [1] found that the computational effort using L = 4 or 5 is practically the same as L = L max in a grid with N = 129 Â 129 points; [36] suggested no less than four levels in a two-dimensional advection-diffusion problem. These analyses show that the parameter number of levels (L) is not modified in problems with two equations using FAS and CS schemes.…”

“…They found g opt = 3 or 4 as parameters that minimized the amount of CPU time. In [34], tests were performed with three solvers in the same equation (for the MSI solver used in this work); they found that g opt = 1 or 2 for the CS scheme and g opt = 4 in the case of the FAS scheme. These results show that the coupling equations, compared with the Laplace equation, do not influence the optimum number of inner iterations.…”

Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

“…High-order scheme always plays an important role in DNS of compressible boundary layer turbulence, especially at high Reynolds or with high Mach number. In order to numerically simulate such complex flow, various high-order and high resolutive schemes [3][4][5][6][7] have been developed in past decades. No doubt, WENO [8][9][10] and it's derived schemes are of the most successful ones.…”

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

“…HOC difference schemes have been developed and applied to a variety of elliptic equations, the incompressible Navier-Stokes equations and Stokes problems by many authors [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], because they not only provide accurate numerical results and save computational work, but also are easier to deal with boundary conditions. Although an EHOC scheme has been proposed to solve effectively the MHD duct flow problems with low-to-high Ha in [27] very recently, to the best of authors' knowledge, there is still no any report about the implementation of the HOC difference scheme on non-uniform space grids to solve the MHD duct flow problems.…”