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Kutta Scheme (kutta + scheme)

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Engineering100%

Selected Abstracts

Quasi-wavelet solution of diffusion problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2004
Tang Jiashi
Abstract A new method, quasi-wavelet method, is introduced for solving partial differential equations of diffusion which are important to chemical and mechanical engineering. A new scheme for the extension of boundary conditions is proposed. The quasi-wavelet method is utilized to discretize the spatial derivatives, while the Runge,Kutta scheme is employed for the time advancing. The problems of particle diffusion in the electrochemistry reaction and temperature diffusion in plates are studied. Quasi-wavelet solution of the former problem is compared with those of a finite difference method. Solution of the latter problem is calibrated by analytical solution. Numerical results indicate that the quasi-wavelet approach is very robust and efficient for diffusion problems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

High-order ENO and WENO schemes for unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2007
W. R. Wolf
Abstract This work describes the implementation and analysis of high-order accurate schemes applied to high-speed flows on unstructured grids. The class of essentially non-oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of third- and fourth-order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2-D Euler equations in a cell centred finite volume context. High-order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge,Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high-order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high-speed flow simulations are presented with the objective of assessing the implemented capability. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Lyapunov spectrum determination from the FEM simulation of a chaotic advecting flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006
Philippe CarrièreArticle first published online: 7 SEP 200
Abstract The problem of the determination of the Lyapunov spectrum in chaotic advection using approximated velocity fields resulting from a standard FEM method is investigated. A fourth order Runge,Kutta scheme for trajectory integration is combined with a third order Jacobian matrix method with QR -factorization. After checking the algorithm on the standard Lorenz and coupled quartic oscillator systems, the method is applied to a model 3-D steady flow for which an analytical expression is known. Both linear and quadratic approximated velocity fields succeed in predicting the Lyapunov exponents as well as describing the chaotic or regular regions inside the flow with satisfactory accuracy. A more realistic flow is then studied in order to delineate the possible limitations of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Non-oscillatory relaxation methods for the shallow-water equations in one and two space dimensions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2004
Mohammed Seaïd
Abstract In this paper, a new family of high-order relaxation methods is constructed. These methods combine general higher-order reconstruction for spatial discretization and higher order implicit-explicit schemes or TVD Runge,Kutta schemes for time integration of relaxing systems. The new methods retain all the attractive features of classical relaxation schemes such as neither Riemann solvers nor characteristic decomposition are needed. Numerical experiments with the shallow-water equations in both one and two space dimensions on flat and non-flat topography demonstrate the high resolution and the ability of our relaxation schemes to better resolve the solution in the presence of shocks and dry areas without using either Riemann solvers or front tracking techniques. Copyright © 2004 John Wiley & Sons, Ltd. [source]