scholarly journals An analytical verification test for numerically simulated convective flow above a thermally heterogeneous surface

2015 ◽  
Vol 8 (6) ◽  
pp. 1809-1819 ◽  
Author(s):  
A. Shapiro ◽  
E. Fedorovich ◽  
J. A. Gibbs
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Numerical Algorithms ◽  
Boussinesq Equations ◽  
Thermal Forcing ◽  
Pressure Poisson Equation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Buoyancy Driven Flows ◽  
Boussinesq Fluid

Abstract. An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. This analytical solution is one of the few available for wall-bounded buoyancy-driven flows. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free of errors in formulation of wall boundary conditions and to evaluate the relative performances of competing numerical algorithms. Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be for testing the no-slip, impermeable wall boundary conditions for the pressure Poisson equation. Examples of such tests are presented.

scholarly journals An analytical verification test for numerically simulated convective flow above a thermally heterogeneous surface

2015 ◽  
Vol 8 (3) ◽  
pp. 2847-2873
Author(s):  
A. Shapiro ◽  
E. Fedorovich ◽  
J. A. Gibbs
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithms ◽  
Boussinesq Equations ◽  
Thermal Forcing ◽  
Pressure Poisson Equation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Computer Codes ◽  
Verification Test ◽  
Boussinesq Fluid

Abstract. An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free of errors in formulation of wall boundary conditions, and to evaluate the relative performances of competing numerical algorithms. Because the solution pertains to flows driven by a surface thermal forcing, one of its main applications may be for testing the no-slip, impermeable wall boundary conditions for the pressure Poisson equation. Examples of such tests are presented.

Improved wall boundary conditions in the incompressible smoothed particle hydrodynamics method

2018 ◽  
Vol 28 (3) ◽  
pp. 704-725 ◽  
Author(s):  
Tuan Minh Nguyen ◽  
Abdelraheem M. Aly ◽  
Sang-Wook Lee
Keyword(s):  
Boundary Conditions ◽  
Smoothed Particle Hydrodynamics ◽  
Benchmark Problems ◽  
Content Type ◽  
Pressure Poisson Equation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics

Purpose The purpose of this paper is to improve the 2D incompressible smoothed particle hydrodynamics (ISPH) method by working on the wall boundary conditions in ISPH method. Here, two different wall boundary conditions in ISPH method including dummy wall particles and analytical kernel renormalization wall boundary conditions have been discussed in details. Design/methodology/approach The ISPH algorithm based on the projection method with a divergence velocity condition with improved boundary conditions has been adapted. Findings The authors tested the current ISPH method with the improved boundary conditions by a lid-driven cavity for different Reynolds number 100 ≤ Re ≤ 1,000. The results are well validated with the benchmark problems. Originality/value In the case of dummy wall boundary particles, the homogeneous Newman boundary condition was applied in solving the linear systems of pressure Poisson equation. In the case of renormalization wall boundary conditions, the authors analytically computed the renormalization factor and its gradient based on a quintic kernel function.

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