Yazar "Shashkov, Mikhail" seçeneğine göre listele

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    Locally exact smooth reconstruction of lines, circles, planes, spheres, cylinders and cones by blending successive circular interpolants
    (Selcuk University Research Center of Applied Mathematics, 2002) Liska, Richard; Shashkov, Mikhail; Swartz, Blair
    G-smooth curves and surfaces are developed to span a given logically cuboid distribution of nodes. Given appropriate data, they locally reconstruct the curves and surfaces of spherical or cylindrical coordinates. Thus, if a set of nodes consists of a contiguous subset of a tensor product grid of points associated with a (possibly non-uniform) set of coordinate values of some rectangular, cylindrical, or spherical coordinate system; then the appropriate coordinate curves (linear or circular segments) and coordinate surfaces (segments of planes, cylinders, spheres and cones) that interpolate the subset are reconstructed exactly. The underlying construction uses four successive nodes to define a curve spanning the middle pair as follows: One interpolates each of the two successive triples of nodes with the segment of a circle or straight line going through these three points. Then one blends the two segments continuously between the middle pair of nodes. The blend is relatively linear in terms of arc-length along each segment. The union of such successive curve-sections forms a G curve. Wire-frames of such curves define cell edges. Similar intermediate curvilinear interpolation of the wires defines cell faces, and their union defines G coordinate-like surfaces. The surface generated depends on the direction one interpolates the wires. If the nodes are a tensor product grid associated with a sufficiently smooth reference coordinate system, then the cell edges (and probably also the cell faces) are third-order accurate.
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    Optimization-based reference-matrix rezone strategies for arbitrary Lagrangian-Eulerian methods on unstructured meshes
    (Selcuk University Research Center of Applied Mathematics, 2002) Shashkov, Mikhail; Knupp, Patrick
    The objective of the Arbitrary Lagrangian-Eulerian (ALE) methodology for solving multidimensional fluid flow problems is to move the computational mesh, using the flow as a guide, to improve the robustness, accuracy and efficiency of the simulation. A principal element is the rezone phase in which the computational ("rezoned") mesh is created that is adapted to the fluid motion. Here we describe a general rezone strategy that ensures the geometric quality of the computational mesh, while keeping it as close as possible to the Lagrangian mesh. In terminology of mesh generation community our method can be classified as a two-stage smoothing algorithm. We provide numerical examples to demonstrate the robustness and the effectiveness of our methodology.
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    Support operator method for Laplace equation on unstructured triangular grid
    (Selcuk University Research Center of Applied Mathematics, 2002) Ganzha, Victor G.; Liska, Richard; Shashkov, Mikhail; Zenger, Christoph
    A finite difference algorithm for solution of generalized Laplace equation on unstructured triangular grid is constructed by a support operator method. The support operator method first constructs discrete divergence operator from the divergence theorem and then constructs discrete gradient operator as the adjoint operator of the divergence. The adjointness of the operators is based on the continuum Green formulas which remain valid also for discrete operators. Developed method is exact for linear solution and has second order convergence rate. It is working well for discontinuous diffusion coefficient and very rough or very distorted grids which appear quite often e.~g. in Lagrangian simulations. Being formulated on the unstructured grid the method can be used on the region of arbitrary geometry shape. Numerical results confirm these properties of the developed method.