Numerical Results for a Discrete Duality Finite Volume Discretization Applied to the Navier–Stokes Equations

2017 ◽  
pp. 141-161 ◽  
Author(s):  
Sarah Delcourte ◽  
Pascal Omnes
Keyword(s):  
Finite Volume ◽  
Stokes Equations ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Discretization

On the Immersed Boundary Method: Finite Element Versus Finite Volume Approach

2012 ◽  
Author(s):  
Angelo Frisani ◽  
Yassin A. Hassan
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Finite Volume ◽  
Stokes Equations ◽  
Numerical Results ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow

A projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations in conjunction with the Immersed Boundary Method (IBM) for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body fitted mesh. The no-slip boundary constraint is satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the incompressible Navier-Stokes equations as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The projection operation removes the immersed boundary surface slip and non-divergence-free components of the velocity field. The boundary force is determined implicitly at the inner iterations of the fractional step method implemented. No constitutive relations for the immersed boundary objects fluid interaction are required, allowing the formulation introduced to use larger CFL numbers compared to previous methodologies. An overview of the immersed boundary approach is presented showing third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution using the Immersed Finite Element Method (IFEM). For the Immersed Finite Volume Method (IFVM) a ghost-cell approach is used. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the analytical solution. The numerical results are compared with the analytical solution also for adaptive mesh refinement (for the IFEM) showing an excellent error reduction. Computations were performed using IFEM and IFVM approaches for the time-dependent incompressible Navier-Stokes equations in a two-dimensional flow past a stationary circular cylinder at Re = 20, and 40, where shedding effects are not present. The drag coefficient and the recirculation length error compared to the experimental data is less than 3–4%. Simulations for the two-dimensional flow past a stationary circular cylinder at Re = 100 were also performed. For Re numbers above 46, unsteadiness generates vortex shedding, and an unsteady flow regime is present. The results shown are in excellent quantitative and qualitative agreement with the flow pattern expected. The numerical results obtained with the discussed IFEM and IFVM were also compared against other immersed boundary methodologies available in literature and simulation performed with the commercial computational fluid dynamics code STAR-CCM+/V5.02.009 for which a body fitted finite volume numerical discretization was used. The benchmark showed that the numerical results obtained with the implemented immersed boundary methods are very close to those obtained from STAR-CCM+ with a very fine mesh and in a good agreement with the other IBM techniques. The IBM based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.

scholarly journals Aerodynamic and thermal environment of a gap under hypersonic flight

2018 ◽  
Vol 22 (4) ◽  
pp. 1753-1758
Author(s):  
Haiming Huang ◽  
Jin Guo ◽  
Guo Huang
Keyword(s):  
Heat Transfer ◽  
Finite Volume ◽  
Stokes Equations ◽  
Thermal Environment ◽  
Numerical Results ◽  
Navier Stokes ◽  
Finite Volume Schemes ◽  
Navier Stokes Equations ◽  
Leading Role ◽  
Volume Method

Accurate prediction of aerodynamic and thermal environment around a gap has a significant effect on the development of spacecraft. The implicit finite volume schemes are derived and programmed from Navier-Stokes equations. Taking the gap between thermal insulation tiles as an example, a numerical simulation is performed by the finite volume method to obtain the flow characteristic in a gap and then to analyze the heat transfer mechanism. The numerical results are consistent with the experimental ones, which prove the precision of the method used in this paper. Furthermore, the numerical results reveal that the heat convection plays a leading role in heat transfer around a gap.

Assessment of CFD Techniques for Wind Turbine Aeroelasticity

2006 ◽  
Author(s):  
Ce´dric Liauzun
Keyword(s):  
Wind Tunnel ◽  
Wind Turbine ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Excitation Frequencies

Two CFD techniques are assessed aiming at wind turbine aeroelasticity: a classic finite volume formulation to solve the Navier-Stokes equations, and a viscous-inviscid interaction formulation. Those 2 methods are tested with a NACA 634 – 421 airfoil, and both steady and unsteady numerical results are compared with experiments performed in the IAT wind tunnel. The Naviers-Stokes solver associated with the Wilcox k–ω turbulence model with SST corrections gives pretty good predictions for incidence in the range 0–15°, even for the static stall at 9°. The viscous-inviscid interaction solver provides results very close to the experiments for the whole range of incidence (0–30°). As far as unsteady simulations are concerned, both solvers give similar results. The computed lift evolutions versus incidence and excitation frequencies reproduce fairly well the experimental ones.

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