Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. (English) Zbl 1465.65116
The authors present a finite volume method for the diffusion equations that can be applied to general polyhedral meshes. It is based on the flux balanced approximation using the least-squares gradient with the distance weighted harmonic mean of piecewise continuous diffusion coefficient. The degrees of freedom are the values at the centers of the cells. The flux balanced approximation is proposed without numerically computing the gradient itself at the faces of computational cells in order to find a normal diffusive flux. It is shown that in the case of discontinuous diffusion coefficient, it is suitable to use the restricted least-squares gradient that respects the discontinuity in the approximation. The method can be used in the iterative way, where each iteration uses a matrix in the 1-ring neighborhood. Several numerical examples are presented to illustrate some advantages of the proposed method.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65K10 | Numerical optimization and variational techniques |
| 65F10 | Iterative numerical methods for linear systems |
| 65Y10 | Numerical algorithms for specific classes of architectures |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 35Q94 | PDEs in connection with information and communication |
Keywords:
diffusion equations; finite volume methods; polyhedral mesh; least-squares gradient; deferred correction; cross diffusionReferences:
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