# American Institute of Mathematical Sciences

March  2021, 14(3): 785-801. doi: 10.3934/dcdss.2020333

## Numerical evaluation of artificial boundary condition for wall-bounded stably stratified flows

 1 Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovo Náměstí 13,121 35 Prague 2, Czech Republic 2 Institute of Mathematics, Czech Academy of Sciences, Žitná 25,115 67 Prague 1, Czech Republic 3 Mediterranean Institute of Oceanography - MIO, UM 110 USTV - AMU - CNRS/INSU 7294 - IRD 235, Université de Toulon, BP 20132 F-83957 La Garde cedex, France 4 Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83,186 75 Prague 8, Czech Republic

* Corresponding author: Petr Knobloch

Received  January 2019 Revised  November 2019 Published  March 2021 Early access  April 2020

The paper presents a numerical study of the efficiency of the newly proposed far-field boundary simulations of wall-bounded, stably stratified flows. The comparison of numerical solutions obtained on large and truncated computational domain demonstrates how the solution is affected by the adopted far-field conditions. The mathematical model is based on Boussinesq approximation for stably stratified viscous variable density incompressible fluid. The three-dimensional numerical simulations of the steady flow over an isolated hill were performed using a high-resolution compact finite difference code, with artificial compressibility method used for pressure computation. The mutual comparison of the full domain reference solution and the truncated domain solution is provided and the influence of the newly proposed far-field boundary condition is discussed.

Citation: Tomáš Bodnár, Philippe Fraunié, Petr Knobloch, Hynek Řezníček. Numerical evaluation of artificial boundary condition for wall-bounded stably stratified flows. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 785-801. doi: 10.3934/dcdss.2020333
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##### References:
Vertical velocity contours and flow streamlines in the plane of symmetry
Vertical velocity isosurfaces
Vertical velocity contours in the plane of symmetry - truncated solution
Vertical velocity contours in the plane of symmetry - truncated domain - $\frac{\partial p}{\partial n} = 0$
Contours of the transversal velocity component $v$ and flow streamlines
Contours of the vertical velocity component $w$ and flow streamlines
Isosurfaces of the transversal velocity component $v$
Isosurfaces of the vertical velocity component $w$
Computational domain and its extension
Inlet velocity profile setup
Contours of the transversal velocity component $v$ - nondimensionalized $\widetilde{v} = v/U_{*}$
Contours of the vertical velocity component $w$ - nondimensionalized $\widetilde{w} = w/U_{*}$
Isosurfaces of the transversal velocity component $v$ - nondimensionalized $\widetilde{v} = v/U_{*}$
Isosurfaces of the vertical velocity component $w$ - nondimensionalized $\widetilde{w} = w/U_{*}$
Pressure contours in the plane of symmetry
Longitudinal velocity contours in the plane of symmetry
Vertical velocity contours in the plane of symmetry
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