A Multiresolution Model for the Simulation of Transient Heat and Mass Transfer

Abstract

The development of an efficient computational methodology for transient heat and mass transfer applications is challenging. When a solution is localized on the fraction of a computational domain, an appropriate adaptive mesh method could minimize computational work. In this paper, we propose a novel adaptive-mesh multi-resolution algorithm for the transient momentum and energy equations. The nonlinear dynamics between the velocity and temperature fields is modeled by solving the coupled system of equations simultaneously, where the rate of convergence has been optimized so that computational cost remains proportional to the number of grid points. Numerical experiments have exhibited good agreements with benchmark simulation data.

A computational methodology for two‐dimensional fluid flows

“…Although Knoll and Keyes [65] have reviewed this approach of solving nonlinear system of equations for multiphysics problems, in the area of CFD, it is not a commonly adopted technique (see also [22]). Numerical experiments suggested that Á 6 10 4 is sufficient for this example.…”

“…A solution is often obtained by evaluating the integral of the charge distribution using the fast multiple method [17], and this technique is also used by the vortex method algorithm [18,19]. [20]) may also be obtained from the implicit in time discretization of the momentum equation [1,[21][22][23][24]. A 'Poisson-like' nonlinear vector equation (or nonlinear Poisson equation, e.g.…”

“…[22]), the scalar Poisson equation takes more computational overhead than the accompanying vector advectiondiffusion equation of the system (see [7] for a comprehensive review). Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to approximate a fluid flow.…”

“…[22]), the scalar Poisson equation takes more computational overhead than the accompanying vector advectiondiffusion equation of the system (see [7] for a comprehensive review). [22]), the scalar Poisson equation takes more computational overhead than the accompanying vector advectiondiffusion equation of the system (see [7] for a comprehensive review).…”

“…The computed streamlines and the velocity fields have been demonstrated.[9]-provides a rapid computing algorithm, in heat and mass transfer analysis (e.g. [22]), the scalar Poisson equation takes more computational overhead than the accompanying vector advectiondiffusion equation of the system (see [7] for a comprehensive review). Many other authors show a growing interest on improving computational efficiency for similar problems [4,[25][26][27][28][29][30].In the present approach, we discretize the set of nonlinear partial differential equations (PDEs), governing the conservation of mass, momentum and enrgy of a fluid flow with the implicit Crank-Nicolson method, which leads to a nonlinear system of 'Poisson-like' equations.…”