Abstract
We present in this paper a numerical scheme for incompressible Navier-Stokes equations with open boundary conditions, in the framework of the pressure and velocity correction schemes. In Poux et al. (J Comput Phys 230:4011–4027, 2011), the authors presented an almost second-order accurate version of the open boundary condition with a pressure-correction scheme in finite volume framework. This paper proposes an extension of this method in spectral element method framework for both pressure- and velocity-correction schemes. A new way to enforce this type of boundary condition is proposed and provides a pressure and velocity convergence rate in space and time higher than with the present state of the art. We illustrate this result by computing some numerical tests.
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Notes
- 1.
Ideally, χ = 1 but as Guermond proved [8], for stability issues, χ is necessarily strictly lower than 2μ∕d.
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Acknowledgements
The second author would like to thank Professor Claudio Canuto for many discussions which allowed improving the presentation of this method.
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Ahusborde, E., Azaïez, M., Glockner, S., Poux, A. (2014). A Contribution to the Outflow Boundary Conditions for Navier-Stokes Time-Splitting Methods. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_5
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DOI: https://doi.org/10.1007/978-3-319-01601-6_5
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