GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
Support-operator finite-difference algorithms for general elliptic problems
Journal of Computational Physics
Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A finite volume method for the approximation of diffusion operators on distorted meshes
Journal of Computational Physics
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
Journal of Computational Physics
The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
Journal of Computational Physics
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes
SIAM Journal on Scientific Computing
High-order mimetic finite difference method for diffusion problems on polygonal meshes
Journal of Computational Physics
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Journal of Computational Physics
Local flux mimetic finite difference methods
Numerische Mathematik
Journal of Computational Physics
A finite volume method for approximating 3D diffusion operators on general meshes
Journal of Computational Physics
Journal of Computational Physics
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In this paper, we describe a second-order accurate cell-centered finite volume method for solving anisotropic diffusion on two-dimensional unstructured grids. The resulting numerical scheme, named CCLAD (Cell-Centered LAgrangian Diffusion), is characterized by a local stencil and cell-centered unknowns. It is devoted to the resolution of diffusion equation on distorted grids in the context of Lagrangian hydrodynamics wherein a strong coupling occurs between gas dynamics and diffusion. The space discretization relies on the introduction of two half-edge normal fluxes and two half-edge temperatures per cell interface using the partition of each cell into sub-cells. For each cell, the two half-edge normal fluxes attached to a node are expressed in terms of the half-edge temperatures impinging at this node and the cell-centered temperature. This local flux approximation can be derived through the use of either a sub-cell variational formulation or a finite difference approximation, leading to the two variants CCLADS and CCLADNS. The elimination of the half-edge temperatures is performed locally at each node by solving a small linear system which is obtained by enforcing the continuity condition of the normal heat flux across sub-cell interface impinging at the node. The accuracy and the robustness of the present scheme is assessed by means of various numerical test cases.