In many fluid dynamics problems the boundary conditions may be unknown, or the domain may be unbounded. Also mass conservation and stability with respect to dominating convection is substantial. Therefore, we test two coupling methods to address these issues on the prototype of a flow and transport problem. More precisely, we couple the vertex-centered and the cell-centered finite volume method with the boundary element method, FVM-BEM and CFVM-BEM, respectively. Also robust refinement indicators are considered which allow us to steer an adaptive mesh-refinement algorithm to treat efficiently problems with singularities or boundary/internal layers—shown on two examples.
- Boundary Element Method
- Finite Volume Method
- Finite Volume Scheme
- Exterior Problem
- Interior Domain
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Erath, C.: Coupling of the finite volume element method and the boundary element method: an a priori convergence result. SIAM J. Numer. Anal. 50(2), 574–594 (2012)
Erath, C.: A new conservative numerical scheme for flow problems on unstructured grids and unbounded domains. J. Comput. Phys. 245, 476–492 (2013)
Erath, C.: A posteriori error estimates and adaptive mesh refinement for the coupling of the finite volume method and the boundary element method. SIAM J. Numer. Anal. 51(3), 1777–1804 (2013)
Erath, C., Praetorius, D.: A posteriori error estimate and adaptive mesh refinement for the cell-centered finite volume method for elliptic boundary value problems. SIAM J. Numer. Anal. 47(1), 109–135 (2008)
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Erath, C. (2014). Comparison of Two Couplings of the Finite Volume Method and the Boundary Element Method. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05683-8
Online ISBN: 978-3-319-05684-5
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