Accession Number : ADA294750
Title : Finite Volume Element (FVE) Discretization and Multilevel Solution of the Axisymmetric Heat Equation.
Descriptive Note : Master's thesis,
Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Personal Author(s) : Litaker, Eric T.
PDF Url : ADA294750
Report Date : DEC 1994
Pagination or Media Count : 117
Abstract : The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed. (AN)
Descriptors : *MATHEMATICAL MODELS, *FINITE DIFFERENCE THEORY, *NAVIER STOKES EQUATIONS, ALGORITHMS, VOLUME, COMPUTATIONS, TIME DEPENDENCE, MATRICES(MATHEMATICS), FINITE ELEMENT ANALYSIS, COMPARISON, THESES, PROBLEM SOLVING, MATHEMATICAL PROGRAMMING, GRIDS(COORDINATES), SOLUTIONS(GENERAL), CYLINDRICAL BODIES, INTERPOLATION, AXISYMMETRIC, CONVERGENCE, TWO DIMENSIONAL FLOW, HEAT FLUX, ITERATIONS, DISCRETE FOURIER TRANSFORMS, ASYMPTOTIC NORMALITY.
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE