Abstract
A modified cubic Petrov-Galerkin method for solution of multidimensional unsteady advection-diffusion problems is proposed. The method is based on a weighted residual formulation in which the trial space is piecewise linear and the test space is a special piecewise cubic space. The test functions are formed by adding a symmetric cubic perturbation to the piecewise linear basis functions. A frequency-fitting algorithm is used to determine the appropriate magnitude of the cubic perturbation. With this frequency fitted parameter, the method is shown to be superior to standard Galerkin and Petrov-Galerkin methods. Both one- and two-dimensional numerical results are presented. The two-dimensional results are for a rotating flow field and demonstrate that the method performs very well in nonconstant velocity fields. The numerical results demonstrate that the accuracy of the cubic Petrov-Galerkin method is comparable to that of a quadratic basis function Galerkin method, with less than half the computational effort.
Original language | English (US) |
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Pages (from-to) | 289-308 |
Number of pages | 20 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 92 |
Issue number | 3 |
DOIs | |
State | Published - Nov 1991 |
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications