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Unified Coordinate System, Multi-media, Computational Fluid Dynamics

Posted on:2006-05-11Degree:DoctorType:Dissertation
Country:ChinaCandidate:P Y JiaFull Text:PDF
GTID:1110360155468151Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
Recently, Hui introduced a so-called unified coordinate system for compressible single-fluid computations. In this system, the flow variables are considered to be functions oftime and of some permanent identification of pseudo - particles which move with velocityhq, q being the velocity of fluid particles. It includes the Eulerian coordinates as specialcase when h = 0 and the Lagrangian when h = 1. For two-dimensional inviscid flow, the free function h is chosen so as to preserve grid angles. This results in a coordinate system which avoids excessive numerical diffusion across slip lines in Eulerian coordinates and avoids severe grid deformation in Lagrangian coordinates, yet it retains sharp resolution of slip lines. In the dissertation, we extend two-dimensional single-fluid computations to multimaterial fluid computations in the unified coordinate system. We discuss the form andhyperbolicity of the y -based extended Euler equations in the unified coordinate, and givethe solution to the Riemann problem for the 1-D extended Euler equations obtained from the 2-D extended Euler equations after dimensional splitting. The 2-D extended Euler equations are numerically solved using the Godunov scheme with MUSCL update. The numerical tests show the advantages of the unified coordinate. Moreover, we use a moving mesh method other than preserving grid angles for determination of h. Numerical results show good efficiency and accuracy of the method. In the latter part of the dissertation, we give the Jacobian matrix, eigenvalues and corresponding eigenvectors for the 1-D extended Euler equations in the unified coordinate, and solve the equations applying a second-order accurate, two-step TVD scheme. The scheme does not necessitate the characteristic decompositions of the usual TVD schemes. A few numerical results show simplicity and practicability of the scheme, and show the advantages of the unified coordinate.
Keywords/Search Tags:Unified coordinate, multimaterial flow, extended Euler equations, moving mesh method, Godunov-type scheme, TVD scheme
PDF Full Text Request
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