Application of Multigrid Methods for Integral Equations to Two Problems from Fluid Dynamics
Abstract
Multigrid methods are applied in order to solve efficiently the nonsparse systems of equations that occur in the numerical solution of the following problems from fluid dynamics: (1) calculation of potential flow around bodies and (2) calculation of oscillating disk flow. Problem (1) is reformulated as a boundary integral equation of the second kind that is approximated by a firstorder panel method resulting in a full system of equations. This method is in widespread use for aerodynamic computations. The second problem is described by the NavierStokes and continuity equations. By means of the von Kármán similarity transformations these equations are reduced to a nonlinear system of parabolic equations which are approximated by implicit finite difference techniques. From the periodic conditions in time one obtains a nonsparse system of equations. For these two problems from fluid dynamics the fast convergence of multigrid methods for integral equations is established by numerical experiments.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 1982
 DOI:
 10.1016/00219991(82)900614
 Bibcode:
 1982JCoPh..48..441S
 Keywords:

 Computational Fluid Dynamics;
 Coordinates;
 Finite Difference Theory;
 Fredholm Equations;
 Iterative Solution;
 Panel Method (Fluid Dynamics);
 Boundary Integral Method;
 Continuity Equation;
 NavierStokes Equation;
 Oscillating Flow;
 Parabolic Differential Equations;
 Potential Flow;
 Von Karman Equation;
 Fluid Mechanics and Heat Transfer