scholarly journals A higher order scheme for two-dimensional quasi-static crack growth simulations

2007 ◽  
Vol 196 (21-24) ◽  
pp. 2527-2538 ◽  
Author(s):  
Jonas Englund
Keyword(s):  
Crack Growth ◽  
Higher Order ◽  
Two Dimensional ◽  
Static Crack ◽  
Order Scheme ◽  
Higher Order Scheme

Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-Diffusion Equations

2011 ◽  
Vol 9 (4) ◽  
pp. 897-916 ◽  
Author(s):  
Y. V. S. S. Sanyasiraju ◽  
Nachiketa Mishra
Keyword(s):  
Coefficient Matrix ◽  
Higher Order ◽  
Diffusion Equations ◽  
Wave Number ◽  
Two Dimensional ◽  
Thomas Algorithm ◽  
Convection Diffusion ◽  
Numerous Model ◽  
Order Scheme ◽  
Higher Order Scheme

AbstractThis paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coefficients. The scheme is for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For two-dimensional problems, the scheme produces an accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary.

A Compact Higher-Order Scheme for Two-Dimensional Unsteady Convection–Diffusion Equations

2019 ◽  
Vol 17 (07) ◽  
pp. 1950025
Author(s):  
Yon-Chol Kim
Keyword(s):  
Stability Analysis ◽  
Numerical Study ◽  
Higher Order ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Order Scheme ◽  
Higher Order Scheme ◽  
Convection Dominated ◽  
Diffusion Problems

In this paper, we study a compact higher-order scheme for the two-dimensional unsteady convection–diffusion problems using the nearly analytic discrete method (NADM), especially, focusing on the convection dominated-diffusion problems. The numerical scheme is constructed and the stability analysis is implemented. We find the order of accuracy of scheme is [Formula: see text], where [Formula: see text] is the size of time steps and [Formula: see text] the size of spacial steps, especially, making clear the relation between [Formula: see text] and [Formula: see text] is according to the different values of diffusion parameter [Formula: see text] through von Neumann stability analysis. The obtained numerical results for several benchmark problems show that our method makes progress in the numerical study of NADM for convection–diffusion equation and is to be effective and helpful particularly in computations for the convection dominated-diffusion equations and, furthermore, valuable in the numerical treatment of many real-world problems such as MHD natural convection flow.

A Parallel HOFD Scheme for Direct Numerical Simulation of Turbulent Magnetically Driven Flows

2001 ◽  
Author(s):  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Parallel Machines ◽  
Higher Order ◽  
Electrically Conducting ◽  
Wide Range ◽  
Order Scheme ◽  
Higher Order Scheme

Abstract Turbulent magnetically flows occur in a wide range of material processing systems involving electrically conducting melts. This paper presents a parallel higher order scheme for the direct numerical simulation of turbulent magnetically driven flows in induction channels. The numerical method is based on the higher order finite difference algorithm, which enjoys the spectral accuracy while minimizing the computational intensity. This, coupled with the parallel computing strategy, provides a very useful means to simulate turbulent flows. The higher order finite difference formulation of magnetically driven flow problems is described in this paper. The details of the parallel algorithm and its implementation for the simulations on parallel machines are discussed. The accuracy and numerical performance of the higher order finite difference scheme are assessed in comparison with the spectral method. The examples of turbulent magnetically driven flows in induction channels and pressure gradient driven flows in regular channels are given, and the computed results are compared with experimental measurements wherever possible.

A Parallelized, Dynamic Solution Adaptive, Multi-Grid, Overset Chimera Unstructured Grid Solver

2006 ◽  
Author(s):  
Xiang Zhao ◽  
Sijun Zhang
Keyword(s):  
Computer Code ◽  
General Purpose ◽  
Higher Order ◽  
Flow Problems ◽  
Dynamic Solution ◽  
Convergence Method ◽  
Order Scheme ◽  
Higher Order Scheme ◽  
All Speeds ◽  
Node Solution

This paper presents a parallelized, dynamic solution adaptive, multi-grid, overset Chimera unstructured finite volume solver for all-speed flows. The methods and schemes applicable for all speeds were implemented in the general-purpose CFD computer code. The hanging node solution adaptation, parallel computing algorithm using MPI libraries, overset chimera grid to allow multiple moving bodies calculation and algebraic multi-grid speeding-up convergence method were all facilitated in the solver. With the enhancement of higher order scheme data reconstruction, higher order upwind-biased differencing, multi-pressure-correction, and Bi-CGSTAB and GMRES matrix solvers, the solver can efficiently and accurately handle flow problems in several cases including benchmark and practical.

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