Fundamental Study on High Accurate Environmental Simulation

在本研究项目中，为了模拟环境流动问题，开发了高精度的计算程序。采用变阶线法，在空间和时间上具有较高的精度。该模型采用空间离散化和时间积分相结合的方法构建。在空间离散化中，对流项和扩散项分别采用变阶固有对流格式和改进的微分正交法。这两种离散化技术只需要改变一个参数，就可以得到任意阶的空间精度。并利用龙格-库塔格式对所得到的常微分方程组进行积分。同时，将虚拟边界法引入到该方法中。通常，具有复杂几何形状的流动都是在边界拟合坐标系（BFC）上计算的。然而，BFC系统存在效率不足的问题。在虚拟边界法中，计算是在笛卡尔网格上进行的，而不是在BFC上。此外，为了获得高分辨率，还采用了局部网格细化技术。将该方法应用于圆柱绕流计算，结果与其他计算结果吻合较好。计算时间是均匀笛卡尔网格的2/3倍。然后，在雷诺数Re=1000的范围内，模拟了绕球的流动。Re=1000时，可以重新出现层流向湍流的过渡。模拟了多球绕流过程，结果表明释放的涡是相互作用的。这些结果是由国际会议公开的。结果表明，该方法在环境模拟中具有较好的应用前景。

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.