A new numerical strategy for the resolution of high-Péclet advection-diffusion problems. (English) Zbl 1353.76058
Summary: This paper introduces a discontinuous method for the efficient determination of an approximate numerical solution of the two-dimensional advection-diffusion equation. Using the VTCR methodology (see [P. Ladevèze, C. R. Acad. Sci., Paris, Sér. II, Fasc. b 322, No. 12, 849–856 (1996; Zbl 0920.73113)]), this method involves free-space solutions of the governing partial differential equation. For the advection-diffusion equation with constant coefficients, the free-space solutions are exponential functions with a sharp gradient. The continuity of the solution across element boundaries is enforced weakly through a dedicated variational formulation. Preliminary results for a certain type of benchmark problem suggest that this approach is a promising numerical tool for handling such problems.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Q35 | PDEs in connection with fluid mechanics |
Citations:
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