エネルギ式の熱伝導項の離散化を目的とした歪んだ四角形格子上における有限体積法に関する研究(熱工学,内燃機関,動力など)

概要

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A finite volume method (FVM) on distorted meshes for discretizing energy equation's conduction term is presented. In this method, it is possible to compose the computational mesh of general quadrilateral elements, namely, the cells are not necessarily to be rectangular. Gradient of temperature on the cell's surface is computed to be second-order accurate. Therefore, the error of numerical results by this method is smaller than using traditional multilateral element method (MEM). The error doesn't depend on the degree of mesh distortion. The formulation only based on Taylor's theorem is straightforward. These are advantageous features to revise the fluid flow computation programs (based on FVM) which neglected heat conduction term of energy equation. The test calculations show that the convergence tendency of the numerical error using this method on the distorted mesh is the same as using ordinary 2-node discretization on the constant-interval rectangular mesh. By this method conduction term was added to energy equation of SALE program which had neglected that term originally, and numerical calculation of a fluid flow with heat transfer problem was performed. The numerical result well agrees with the analytical solution.
2010-12-25