Search results for "Stokes equations"
showing 10 items of 49 documents
Fluid–structure interaction of downwind sails: a new computational method
2018
The spreading of high computational resources at very low costs led, over the years, to develop new numerical approaches to simulate the fluid surrounding a sail and to investigate the fluidâstructure interaction. Most methods have concentrated on upwind sails, due to the difficulty of implementing downwind sailing configurations that present, usually, the problem of massive flow separation and large displacements of the sail under wind load. For these reasons, the problem of simulating the fluidâstructure interaction (FSI) on downwind sails is still subject of intensive investigation. In this paper, a new weak coupled procedure between a RANS solver and a FEM one has been implemented t…
Frequency-dependent hydrodynamic interaction between two solid spheres
2017
Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that the compressibility of the…
A High-Resolution Penalization Method for large Mach number Flows in the presence of Obstacles
2009
International audience; A penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkman-penalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this method to theoretical results and to simulations with Fluent software. Our work indicates that this technique can be very promising in applications to complex flows.
Implicit-explicit and explicit projection schemes for the unsteady incompressible Navier–Stokes equations using a high-order dG method
2017
Abstract A modified version of the projection scheme [19] is proposed, which does not show a lower limit for the time step in contrast to the limits of stability observed numerically for some projection type schemes. An advantage of the proposed scheme is that the right-hand side of the Poisson equation for the pressure is independent of the time step. An explicit version of the current scheme is also provided besides the implicit-explicit one. For the implicit-explicit version, we retain divergence of the viscous terms on the right-hand side of the Poisson equation in order to achieve a higher accuracy for low Reynolds number flows. In this way, we also ensure that the Poisson equation wit…
MAST-RT0 solution of the incompressible Navier–Stokes equations in 3D complex domains
2020
A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedr…
Unsteadiness and transition to turbulence in woven spacer filled channels for Membrane Distillation
2017
To characterize the performance of Membrane Distillation (MD) modules, channels filled with woven spacers were investigated by Computational Fluid Dynamics (including Direct Numerical Simulations and the use of the SST k-Ï turbulence model) and by parallel experiments with Thermochromic Liquid Crystals. The cases considered here regard mutually orthogonal filaments with a spacer pitch to channel height ratio P/H=2, two spacer orientations θ with respect to the main flow (0° and 45°), and bulk Reynolds numbers Re from â¼200 to â¼2000, an interval of great interest in practical MD applications. For both values of θ, CFD predicted steady-state flow for Re up to â¼300, and chaotic flow …
Long time behavior for a dissipative shallow water model
2013
We consider the two-dimensional shallow water model derived by Levermore and Sammartino (Nonlinearity 14,2001), describing the motion of an incompressible fluid, confined in a shallow basin, with varying bottom topography. We construct the approximate inertial manifolds for the associated dynamical system and estimate its order. Finally, considering the whole domain R^2 and under suitable conditions on the time dependent forcing term, we prove the L^2 asymptotic decay of the weak solutions.
Navier-Stokes equations on an exterior circular domain: construction of the solution and the zero viscosity limit
1997
Abstract In this Note, we consider the limit of Navier-Stokes equations on a circular domain. By an explicit construction of the solution, it is proved that, when viscosity goes to zero, solution converges to the Euler solution outside the boundary layer and to the Prandtl solution inside the boundary layer.
A stabilized finite element method for particulate two-phase flow equations laminar isothermal flow
1997
A finite element method for the solution of particulate two-phase flows is presented. The governing system has the form of compressible Navier-Stokes equations with unknown pressure. Therefore, the proposed method must capture the main features of stabilized methods used for incompressible as well as for compressible Navier-Stokes equations. Solution of the resulting nonlinear algebraic system of equations is based on the linearization using Newton method in conjunction with Generalized Minimal Residual iterative solver and Incomplete LU preconditioning. The method has been tested for three test cases including venturi tube flow, flow over backward step and mixing of flows in t-junction.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
1992
The tradìtíonal splitting-up method or fractíonal step method is stuítable for sequentìal compulìng. Thís means that the computing of the present fractional step needs the value of the previous fractional steps. In thìs paper we propose a new splitting-up scheme for which the computing of the fractional steps is índependent of each other and therefore can be computed by parallel processors. We have proved the convergence estimates of this scheme both for steady state and nonsteady state linear and nonlinear problems. To use .finite element method to solve Navier-Stokes problems it is always dfficult to handle the zero-divergent finíte element spaces. Here, by using the splitting-up method w…