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Unstructured Triangular Meshes (unstructured + triangular_mesh)
Selected AbstractsMoving meshes, conservation laws and least squares equidistributionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1-2 2002M. J. Baines Abstract In this paper a least squares measure of a residual is minimized to move an unstructured triangular mesh into an optimal position, both for the solution of steady systems of conservation laws and for functional approximation. The result minimizes a least squares measure of an equidistribution norm, which is a norm measuring the uniformity of a fluctuation monitor. The minimization is carried out using a steepest descent approach. Shocks are treated using a mesh with degenerate triangles. Results are shown for a steady-scalar advection problem and two flows governed by the Euler equations of gasdynamics. Copyright © 2002 John Wiley & Sons, Ltd. [source] A second order discontinuous Galerkin method for advection on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2003H. J. M. Geijselaers Abstract In this paper the advection of element data which are linearly distributed inside the elements is addressed. Across element boundaries the data are assumed discontinuous. The equations are discretized by the Discontinuous Galerkin method. For stability and accuracy at large step sizes (large values of the Courant number), the method is extended to second order. Furthermore the equations are enriched with selective implicit terms. This results in an explicit and local advection scheme, which is stable and accurate for Courant numbers less than .95 on unstructured triangle meshes. Results are shown of some pure advection test problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] A visual incompressible magneto-hydrodynamics solver with radiation, mass, and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Necdet AslanArticle first published online: 8 JAN 200 Abstract A visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961,973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical solutions of liquid metal flows by incompressible magneto-hydrodynamics with heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Kenan, entürk Abstract A two-dimensional incompressible magneto-hydrodynamic code is presented in order to solve the steady state or transient magnetized or neutral convection problems with the effect of heat transfer. The code utilizes a numerical matrix distribution scheme that runs on structured or unstructured triangular meshes and employs a dual time-stepping technique with multi-stage Runge,Kutta algorithm. The code can be used to simulate the natural convection with internal heat generation and absorption and nonlinear time-dependent evolution of heated and magnetized liquid metals exposed to external fields. Copyright © 2008 John Wiley & Sons, Ltd. [source] Solution of the hyperbolic mild-slope equation using the finite volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003J. Bokaris Abstract A finite volume solver for the 2D depth-integrated harmonic hyperbolic formulation of the mild-slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild-slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality-free. Copyright © 2003 John Wiley & Sons, Ltd. [source] A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001Victoria Dolean Abstract We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Sparse matrix element topology with application to AMG(e) and preconditioning,NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6-7 2002Panayot S. Vassilevski Abstract This paper defines topology relations of elements treated as overlapping lists of nodes. In particular, the element topology makes use of element faces, element vertices and boundary faces which coincide with the actual (geometrical) faces, vertices and boundary faces in the case of true finite elements. The element topology is used in an agglomeration algorithm to produce agglomerated elements (a non-overlapping partition of the original elements) and their topology is then constructed, thus allowing for recursion. The main part of the algorithms is based on operations on Boolean sparse matrices and the implementation of the algorithms can utilize any available (parallel) sparse matrix format. Applications of the sparse matrix element topology to AMGe (algebraic multigrid for finite element problems), including elementwise constructions of coarse non-linear finite element operators are outlined. An algorithm to generate a block nested dissection ordering of the nodes for generally unstructured finite element meshes is given as well. The coarsening of the element topology is illustrated on a number of fine-grid unstructured triangular meshes. Published in 2002 by John Wiley & Sons, Ltd. [source] | ||||||||||