Comparison ofS andV cycles in multigrid method for linear elliptic equations with variable coefficients

1992 ◽  
Vol 8 (2) ◽  
pp. 113-125 ◽  
Author(s):  
Satteluri R. K. Lyengar ◽  
Anu Goyal
Keyword(s):  
Elliptic Equations ◽  
Multigrid Method ◽  
Variable Coefficients

Method of corrections by higher order differences for elliptic equations with variable coefficients

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Givi Berikelashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Convergence Rate ◽  
Difference Scheme ◽  
Elliptic Equations ◽  
Variable Coefficients ◽  
Order Accuracy ◽  
Corrected Scheme

AbstractWe consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate

Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method

1994 ◽  
Vol 116 (3) ◽  
pp. 435-445 ◽  
Author(s):  
A. Arnone
Keyword(s):  
Multigrid Method ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Maximum Flow ◽  
Variable Coefficients ◽  
Rotating Blade ◽  
A Cell ◽  
Space Discretization ◽  
Transonic Fan ◽  
Full Multigrid Method

A three-dimensional code for rotating blade-row flow analysis has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling for the artificial dissipation. The computational efficiency of a four-stage Runge–Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, nonperiodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

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