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Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. (English) Zbl 07345415
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.
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
Software:
FlowLab; OpenFOAM; AVL
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