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An application of a boundary element method to natural convection |
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| Authors: | K Onishi T Kuroki M Tanaka |
| Institution: | Applied Mathematics Department, Fukuoka University, Fukuoka 814-01, Japan Civil Engineering Department, Fukuoka University, Fukuoka 814-01, Japan Mechanical Engineering Department, Shinshu University, Nagano 380, Japan |
| Abstract: | The direct boundary element method is applied to the numerical modelling of thermal fluid flow in a transient state. The Navier-Stokes equations are considered under the Boussinesq approximation and the viscous thermal flow equations are expressed in terms of stream function, vorticity, and temperature in two dimensions. Boundary integral equations are derived using logarithmic potential and time-dependent heat potential as fundamental solutions. Boundary unknowns are discretized by linear boundary elements and flow domains are divided into a series of triangular cells. Charged points are translated upstream in the numerical evaluation of convective terms. Unknown stream function, vorticity, and temperature are staggered in the computational scheme. Simple iteration is found to converge to the quasi steady-state flow. Boundary solutions for two-dimensional examples at a Reynolds number 100 and Grashoff number 107 are obtained. |
| Keywords: | mathematical model thermal fluid Navier-Stokes equations Boussinesq approximation boundary integral equation upwind scheme bouyancy-driven cavity flow |
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