Study Numerically In Partial Differential Equation Of Sphere

In this thesis, cube-sphere method is adopted to solve partial differential equation ofsphere. This avoids the difficulty of numerically solving partial differential equation in spherecoordination and has great latent capacity in numerical calculation's accuracy and potency.Especially it has great advantage over spectral method in parallel numerical calculation. First the six forms of formulation of shallow water equations and a suite of numericaltest methods are given. Then conformation method of cube-sphere coordination and transformrules between sphere coordination and right-angle coordination and corresponding differentialoperator are given in the thesis. On this basis, the formulations of shallow water equations arededuced from the cube-sphere coordination, using the modified differential quadrature (MDQ)special difference scheme and fourth order Runge-Kutta scheme to solve the shallow waterequations. The vector velocity expressions of six regions in the linear advection ofRossby-Haurwitz wave case and the linear advection of a cosine bell case are given from thecube sphere coordinate. And expressions of six interval's velocity vector are given incube-sphere coordination. An explicit pseudo-viscosicty term ? ?4 was used to free the ( )numerical solutions from the noise introduced at the internal boundaries by the interpolationprocedure. The method is(1) fully explicit (2) fourth order of accuracy in time (3) high orderof accuracy in space by changing only one parameter (4) easy to operate on massively parallelcomputers efficiently, and it is robust in proceeding numerical problem. This thesis is the first time to adopt cube-sphere method in solving numerically partialdifferential equation in our country. The works of the thesis push the numerical weatherforecast's base work forward.