WAVE EQUATION MODEL FOR NUMERICAL SOLUTIONS OF ADVECTION－DOMINANT HEAT TRANSFER

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WAVE EQUATION MODEL FOR NUMERICAL SOLUTIONS OF ADVECTION-DOMINANT HEAT TRANSFER

In this paper the wave equation model (WEM) [1] is extended to solve advection-dominant heat transfer problems in multi-dimensional space. Based on the operator-splitting method the heat transfer equation is divided into an advection equation and a diffusion equation which are solved separately. In advection stage the first order advection equation is transferred to a second order wave equation first, than the wave equation is solved by FEM with mass lumping. The diffusion equation can be solved accurately without many difficulties. A number of numerical examples of multi-dimensional advection are presented in which the advection velocities are non-uniform in space and unsteady in time. The numerical results are quite accurate in comparison with the exact solutions.The mass lumping saves computational effort greatly.