The Study Of 3-D Euler Equations' TVD,ENO Finite Volume Method On Unstructured Meshes

Numerical solution of differential equation contains four steps: modeling, whichconstructs fluid dynamical equations and chooses computational field and boundaryconditions; mesh-generating, which means the mapping and discretization from physicsdomain to computational space; equation discreting, constructs and chooses thenumerical scheme, and analyze the stability and error; outcome submitting, whichpresents the computational results and the reports. The meshes generation has becomemore and more important department, and formation and selection of the computationwill determine the result. This thesis is concerned with the unstructured mesh generationand the using of finite volume method for solving 3-D hyperbolic conservation laws'equations. The following work has been done:(1) We present the idea of domain indicating function which describes thecomputational field, then generate unstructured meshes on three space dimensiondomain, according the scale function based on it. And we also afford the methods forboundary and inner domain boundary approach, mesh optimization, point-source andfaces-source.(2) We give a TVD-type FVM scheme on unstructured meshes. For all the threetypes of spatial discretization discussed in this paper, we used the same timediscretization, namely a high order nonlinearly stable Runge-Kutta time discretizations,which maintains strong stability properties in total variation non-deascreation. In spatialdiscretization, we reconstructed variables polynomials with TVD limiter, and chooseRoe numerical flux and FLLC flux, which maintains physical variable conservations inall space.(3) We introduce the method about ENO-type FVM, then construct an uniformlysecond order accuracy ENO FVM, basing on the principle of composite finite volumemethod, which runs easy.(4) At last, the thesis gives a simplified ENO-type FVM, which introduces the leastsquare idea. We get the value on the simplex cell by the smoothest reconstructedpolynomial, which come from the interpolation polynomial selected by ENO .