A Characteristic Projection Method for Incompressible Thermal Flow

Abstract

This work deals with the computation of incompressible thermal flow under the Boussinesq hypothesis, and a characteristic projection method is proposed for this. First, characteristic temporal discretization is used to obtain an upwind scheme, then at each time step the energy equation can be decoupled from momentum equations. For the remaining Stokes problem we present an improved projection method, which can overcome the numerical boundary-layer problem of the traditional projection method. In conclusion, only three independent linear elliptic equations need to be calculated at each time step; moreover, the stiffness matrices of finite-element approximation are symmetrical, positive, and time-invariant.