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A finite volume method for advection-diffusion problems in convection-dominated regimes.(English)Zbl 1159.76356

Summary: We present a finite volume method for the numerical approximation of advection-diffusion problems in convection-dominated regimes. The method works on unstructured grids formed by convex polygons of any shape and yields a piecewise linear approximation to the exact solution which is second-order accurate away from boundary and internal layers. Basically, we define a constant approximation of the solution gradient in every mesh cell which is expressed by using the cell averages of the solution within the adjacent cells. A careful design of the reconstruction algorithm for cell gradients and the introduction in the discrete formulation of a special non-linear term, which plays the role of the artificial diffusion, allows the method to achieve shock-capturing capability. We emphasize that no slope limiters are required by this approach. Optimal convergence rates, as theoretically expected, and non-oscillatory behavior close to layers are confirmed by numerical experiments.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76R99 Diffusion and convection

Software:

P2MESH;MUMPS

Cite

References:

[1]Amestoy, P.; Puglisi, C., An unsimmetrized LU multifrontal factorization, SIAM J. Matrix Anal. Appl., 24, 2, 553-569 (2002) ·Zbl 1017.65017
[2]P.R. Amestoy, I.S. Duff, J.-Y. L’Excellent, J. Koster, M. Tuma. MUltifrontal Massively Parallel Solver (MUMPS version 4.1) specification sheets. URL: http://graal.ens-lyon.fr/MUMPS/index.html.; P.R. Amestoy, I.S. Duff, J.-Y. L’Excellent, J. Koster, M. Tuma. MUltifrontal Massively Parallel Solver (MUMPS version 4.1) specification sheets. URL: http://graal.ens-lyon.fr/MUMPS/index.html.
[3]T.J. Barth, D.C. Jespersen. The Design and Application of Upwind Schemes on Unstructured Meshes. AIAA Paper 89-0366. AIAA, January 1989.; T.J. Barth, D.C. Jespersen. The Design and Application of Upwind Schemes on Unstructured Meshes. AIAA Paper 89-0366. AIAA, January 1989.
[4]Bertolazzi, E.; Manzini, G., Algorithm 817 P2MESH: generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers, ACM Trans. Math. Software, 28, 1, 101-132 (2002) ·Zbl 1070.65568
[5]Bertolazzi, E.; Manzini, G., A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes, Math. Models Methods Appl. Sci., 8, 1235-1260 (2004) ·Zbl 1079.65113
[6]Bertolazzi, E.; Manzini, G., A second-order maximum principle preserving finite volume method for steady convection-diffusion problems, SIAM, J. Numer. Anal., 43, 5, 2172-2199 (2006) ·Zbl 1145.65326
[7]Bertolazzi, E.; Manzini, G., On vertex reconstructions for cell-centered finite volume approximations of 2-D anisotropic diffusion problems, Math. Models Methods Appl. Sci., 17, 1, 1-32 (2007) ·Zbl 1119.65115
[8]Ciarlet, P. G., The Finite Element Method for Elliptic Problems (1980), North-Holland Publishing Company: North-Holland Publishing Company Amsterdam Holland ·Zbl 0511.65078
[9]Coudière, Y.; Vila, J.-P.; Villedieu, P., Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem, M2AN Math. Model Numer. Anal., 33, 3, 493-516 (1999) ·Zbl 0937.65116
[10]Coudière, Y.; Villedieu, P., Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes, M2AN Math. Model. Numer. Anal., 34, 6, 1123-1149 (1999) ·Zbl 0972.65081
[11]Domelevo, K.; Omnes, P., A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN, Math. Model. Numer. Anal., 39, 6, 1203-1249 (2005) ·Zbl 1086.65108
[12]R. Eymard, T. Gallouët, R. Herbin, The finite volume method, in: P. Ciarlet, J.L. Lions (Ed.), Handbook for Numerical Analysis, North Holland, 2000, pp. 715-1022.; R. Eymard, T. Gallouët, R. Herbin, The finite volume method, in: P. Ciarlet, J.L. Lions (Ed.), Handbook for Numerical Analysis, North Holland, 2000, pp. 715-1022.
[13]Franca, L. P.; Frey, S. L.; Hughes, T. J.R., Stabilized finite element methods: I. Application to the advective-diffusive model, Comput. Methods Appl. Mech. Engrg., 95, 253-276 (1992) ·Zbl 0759.76040
[14]Hermeline, F., A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys., 160, 481-499 (2000) ·Zbl 0949.65101
[15]Hubbard, M. E., Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids, J. Comput. Phys., 155, 1, 54-74 (1999) ·Zbl 0934.65109
[16]Hyman, J.; Shashkov, M.; Steinberg, S., The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials, J. Comput. Phys., 132, 130-148 (1997) ·Zbl 0881.65093
[17]Kershaw, D. S., Differencing of the diffusion equation in Lagrangian hydrodynamics codes, J. Comput. Phys., 39, 375-395 (1981) ·Zbl 0467.76080
[18]C. Le Potier, Schéma volumes finis monotone pour des opérateur de diffusion fortement anisotropes sur des maillages des triangles non structurés, C.R. Acad. Sci. Paris, Ser. I (341) (2005) 787-792.; C. Le Potier, Schéma volumes finis monotone pour des opérateur de diffusion fortement anisotropes sur des maillages des triangles non structurés, C.R. Acad. Sci. Paris, Ser. I (341) (2005) 787-792. ·Zbl 1081.65086
[19]C. Le Potier, Schéma volumes finis pour des opérateur de diffusion fortement anisotropes sur des maillages non structurés, C.R. Acad. Sci. Paris, Ser. I (340) (2005) 921-926.; C. Le Potier, Schéma volumes finis pour des opérateur de diffusion fortement anisotropes sur des maillages non structurés, C.R. Acad. Sci. Paris, Ser. I (340) (2005) 921-926. ·Zbl 1076.76049
[20]A. Mazzia, M. Putti. Extension of second order Godunov mixed method from triangles to tetrahedra, in: R. Herbin, D. Kröner (Ed.), Finite Volumes for Complex Applications III, Problems and Perspectives, Hermes Penton Science, 2002. pp. 413-420.; A. Mazzia, M. Putti. Extension of second order Godunov mixed method from triangles to tetrahedra, in: R. Herbin, D. Kröner (Ed.), Finite Volumes for Complex Applications III, Problems and Perspectives, Hermes Penton Science, 2002. pp. 413-420. ·Zbl 1059.65512
[21]Quarteroni, A.; Valli, A., Numerical Approximation of Partial Differential Equations (1994), Springer-Verlag: Springer-Verlag Berlin ·Zbl 0852.76051
[22]Shashkov, M.; Steinberg, S., Solving diffusion equations with rough coefficients in rough grids, J. Comput. Phys., 129, 383-405 (1997) ·Zbl 0874.65062
[23]Wierse, M., A new theoretically motivated higher order upwind scheme on unstructured grids of simplices, Adv. Comput. Math., 7, 303-335 (1997) ·Zbl 0889.65103
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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