Fundamental Study on High Accurate Environmental Simulation

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In this research project, the high accurate computational codes were developed in order to simulate environmental flow problems. The variable order method of lines (VOMOL) approach is adopted for high accuracy in space and time. The VOMOL is constructed by the spatial discretization and time integration. In the spatial discretization, the variable order proper convective scheme and the modified differential quadrature method are used for the convection and diffusion terms, respectively. Both discretization techniques give the arbitrary order of spatial accuracy by changing only 1 parameter. And the resulting system of ordinary differ ential equations in time is integrated by the Runge-Kutta type scheme. Also, the virtual boundary method is incorporated into the method. Usually, the flows with complicated geometry are computed on the boundary fitted coordinate (BFC) system. However, the BFC system has the lack of efficiency. Instead of the BFC, in the virtual boundary method, the computation is carried out on the Cartesian grid. Moreover, the local mesh refinement technique is used for obtaining the high resolution.The present method is applied to the flows around a circular cylinder and the results are in very good agreement with other computational results. The computational time is 2/3 times the uniform Cartesian grid. Then, the flows around a sphere are simulated up to Reynolds number Re=1000. In Re=1000, the transition from laminar to turbulent flow can be reappeared. The flow around multi-spheres is simulated and the results show that the released vortices are interacted each other.These results are opened by the international conferences. Then, it is concluded that the present method is very promising for the environmental simulations.