# 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  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
##### References:

show all references

##### 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
 [1] Hakan Özadam, Ferruh Özbudak. A note on negacyclic and cyclic codes of length $p^s$ over a finite field of characteristic $p$. Advances in Mathematics of Communications, 2009, 3 (3) : 265-271. doi: 10.3934/amc.2009.3.265 [2] Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 [3] Feng Luo. A combinatorial curvature flow for compact 3-manifolds with boundary. Electronic Research Announcements, 2005, 11: 12-20. [4] Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 [5] Dmitry Treschev. Travelling waves in FPU lattices. Discrete & Continuous Dynamical Systems - A, 2004, 11 (4) : 867-880. doi: 10.3934/dcds.2004.11.867 [6] Arseny Egorov. Morse coding for a Fuchsian group of finite covolume. Journal of Modern Dynamics, 2009, 3 (4) : 637-646. doi: 10.3934/jmd.2009.3.637 [7] Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379 [8] Shu-Yu Hsu. Existence and properties of ancient solutions of the Yamabe flow. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 91-129. doi: 10.3934/dcds.2018005 [9] Matthias Erbar, Jan Maas. Gradient flow structures for discrete porous medium equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1355-1374. doi: 10.3934/dcds.2014.34.1355 [10] Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020027 [11] Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91 [12] Haibo Cui, Haiyan Yin. Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020210 [13] Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 [14] Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035 [15] Pascal Noble, Sebastien Travadel. Non-persistence of roll-waves under viscous perturbations. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 61-70. doi: 10.3934/dcdsb.2001.1.61 [16] Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1 [17] Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 [18] Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044 [19] José Raúl Quintero, Juan Carlos Muñoz Grajales. On the existence and computation of periodic travelling waves for a 2D water wave model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 557-578. doi: 10.3934/cpaa.2018030 [20] M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072

2019 Impact Factor: 1.233