A second order splitting algorithm for thermally‐driven flow problems

Abstract

. (1995). A second order splitting algorithm for thermally-driven flow problems.

Spectral element benchmark simulations of natural convection in two‐dimensional cavities

“…Minev et al [11] describe a spectral element method for thermal problems that, in many respects, is similar to ours. There are some notable di erences though, both in the methodology and in the application to the cavity problem.…”

“…As noted in the Introduction, Minev et al [11] reported computational examples of thermal cavity ows obtained by a spectral element method. In that work only the Nusselt numbers were reported, and the heat ux at the wall was computed by ÿrst-order ÿnite di erences.…”

Numerical Simulation of Buoyant Plumes Using a Fixed Point Iterative Method

“…Numerical simulation has been applied to this kind of flows and results with a 2D Direct Numerical Simulation (DNS) have been reported in [5] and [6]. For the validation of our results we are comparing them with those reported in the cited bibliography.…”

A splitting technique of higher order for the Navier–Stokes equations

“…To achieve a conclusion about the approximation quality ofp n+1 h we compare the right sides of (20) and (22). The derivations on the right side in (22) can be built with a kind of gradient recovery technique to achieve a higher order with the effects discussed above.…”

“…[26,18]. For the boundary conditions of the second-order pressure equation we refer to the discussion in the papers of Karniadakis et al [16], Maday et al [19] and Timmermanns et al [20,23]. For the computation of the pressure boundary conditions in Section 2 we used a variation of the formulation given in [16] by Karniadakis. To use this technique we have to evaluate the laplacian operator with linear finite elements, which leads to a couple of problems that can be avoided using a gradient recovery technique.…”