Abstract
This article introduces a collocated finite-volume method for the incompressible Navier–Stokes equations. Based on the linearity assumption of the velocity and pressure unknowns, the coupled one-sided flux expression is derived. Analysis and correction of the eigenvalues in the matrix coefficients of the vector flux expression result in the inf-sup stable method. A single continuous flux expression follows from the continuity of the one-sided flux approximations. As a result, the conservation for the momentum and the divergence is discretely exact. The method handles general polyhedral meshes but requires an artificial pressure boundary condition for the pressure gradient reconstruction.
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This work was supported by the Russian Science Foundation through the grant 19-71-10094.
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Terekhov, K.M. (2021). Fully-Implicit Collocated Finite-Volume Method for the Unsteady Incompressible Navier–Stokes Problem. In: Garanzha, V.A., Kamenski, L., Si, H. (eds) Numerical Geometry, Grid Generation and Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 143. Springer, Cham. https://doi.org/10.1007/978-3-030-76798-3_23
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