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.

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.

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.

Extension of classical stability theory to viscous planar wall-bounded shear flows

2019 ◽  
Vol 877 ◽  
pp. 1134-1162 ◽  
Author(s):  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Boundary Conditions ◽  
Shear Flows ◽  
Early Stage ◽  
Linear Instability ◽  
Slip Condition ◽  
Translation Invariant ◽  
Alternative Derivation ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Parallel Shear Flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

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