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Incompressible Viscous Flows (incompressible + viscous_flow)
Selected AbstractsNumerical analysis of a 3D hydrodynamic contactINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Costin Alin Caciu Abstract We study here the numerical analysis of a hydrodynamic contact in a particular configuration: the 3D incompressible viscous flow of a fluid dragged by a smooth plate over a rough surface. The mathematical model takes into account and discretizes the local topography of the rough profile. The simulation outcome will be the 3D velocity and pressure fields of the fluid film within the contact borders. This work is limited to the study of numerical resolution methods working solely in finite differences. The algorithms will be tested by analysing and comparing their results with analytically known flows. Copyright © 2006 John Wiley & Sons, Ltd. [source] A new stable space,time formulation for two-dimensional and three-dimensional incompressible viscous flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001Donatien N'dri Abstract A space,time finite element method for the incompressible Navier,Stokes equations in a bounded domain in ,d (with d=2 or 3) is presented. The method is based on the time-discontinuous Galerkin method with the use of simplex-type meshes together with the requirement that the space,time finite element discretization for the velocity and the pressure satisfy the inf,sup stability condition of Brezzi and Babu,ka. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two-dimensional problems are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] A three-dimensional vortex particle-in-cell method for vortex motions in the vicinity of a wallINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2001Chung Ho Liu Abstract A new vortex particle-in-cell method for the simulation of three-dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity,Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd. [source] A computational stream function method for two-dimensional incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005Marcelo H. Kobayashi Abstract This work concerns the development of a numerical method based on the stream function formulation of the Navier,Stokes equations to simulate two-dimensional,plane or axisymmetric,viscous flows. The main features of the proposed method are: the use of the high order finite-difference compact method for the discretization of the stream function equation, the implicit pseudo-transient Newton,Krylov-multigrid matrix free method for the stationary stream function equation and the fourth order Runge,Kutta method for the integration of non-stationary flows. Copyright © 2005 John Wiley & Sons, Ltd. [source] Multi-material incompressible flow simulation using the moment-of-fluid method,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010Samuel P. Schofield Abstract This paper compares the numerical performance of the moment-of-fluid (MOF) interface reconstruction technique with Youngs, LVIRA, power diagram (PD), and Swartz interface reconstruction techniques in the context of a volume-of-fluid (VOF) based finite element projection method for the numerical simulation of variable-density incompressible viscous flows. In pure advection tests with multiple materials MOF shows dramatic improvements in accuracy compared with the other methods. In incompressible flows where density differences determine the flow evolution, all the methods perform similarly for two material flows on structured grids. On unstructured grids, the second-order MOF, LVIRA, and Swartz methods perform similarly and show improvement over the first-order Youngs' and PD methods. For flow simulations with more than two materials, MOF shows increased accuracy in interface positions on coarse meshes. In most cases, the convergence and accuracy of the computed flow solution was not strongly affected by interface reconstruction method. Published in 2009 by John Wiley & Sons, Ltd. [source] A streamfunction,velocity approach for 2D transient incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Jiten C. Kalita Abstract We recently proposed (J. Comput. Phys. 2005; 207(1):52,68) a new paradigm for solving the steady-state two-dimensional (2D) Navier,Stokes (N,S) equations using a streamfunction,velocity (,,v) formulation. This formulation was shown to avoid the difficulties associated with the traditional formulations (primitive variables and streamfunction-vorticity formulations). The new formulation was found to be second-order accurate and was found to yield accurate solutions of a number of fluid flow problems. In this paper, we extend the ideas and propose a second-order implicit, unconditionally stable ,,v formulation for the unsteady incompressible N,S equations. The method is used to solve several 2D time-dependent fluid flow problems, including the flow decayed by viscosity problem with analytical solution, the lid-driven square cavity problem, the backward-facing step problem and the flow past a square prism problem. For the problems with known exact solutions, our coarse grid transient solutions are extremely close to the analytical ones even for high Reynolds numbers (Re). For the driven cavity problem, our time-marching steady-state solutions up to Re=7500 provide excellent matches with established numerical results, and for Re=10000, our study concludes that the asymptotic stable solution is periodic as has been found by other authors in recent studies. For the backward step problem, our numerical results are in excellent agreement with established numerical and experimental results. Finally, for the flow past a square prism, we have very successfully simulated the von Kármán vortex street for Re=200. Copyright © 2009 John Wiley & Sons, Ltd. [source] A level set-based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundaryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Zhijun Tan Abstract A second-order accurate immersed interface method (IIM) is presented for solving the incompressible Navier,Stokes equations with the prescribed velocity at the boundary, which is an extension of the IIM of Le et al. (J. Comput. Phys. 2006; 220:109,138) to a level set representation of the boundary in place of the Lagrangian representation of the boundary using control points on a uniform Cartesian grid. In order to enforce the prescribed velocity boundary condition, the singular forces at the immersed boundary are applied on the fluid. These forces are related to the jump in pressure and the jumps in the derivatives of both the pressure and velocity, and are approximated via using the local Hermite cubic spline interpolation. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier,Stokes equations are discretized via using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by a second-order accurate projection method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate the viscous flows in irregular domains. Copyright © 2009 John Wiley & Sons, Ltd. [source] A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yongtao Wei Abstract A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton,Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] 2D thermal/isothermal incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005Alfredo Nicolás Abstract 2D thermal and isothermal time-dependent incompressible viscous flows are presented in rectangular domains governed by the Boussinesq approximation and Navier,Stokes equations in the stream function,vorticity formulation. The results are obtained with a simple numerical scheme based on a fixed point iterative process applied to the non-linear elliptic systems that result after a second-order time discretization. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the first time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state flows obtained from the unsteady problem. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical simulation of high-Reynolds number flow around circular cylinders by a three-step FEM,BEM modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001D. L. Young Abstract An innovative computational model, developed to simulate high-Reynolds number flow past circular cylinders in two-dimensional incompressible viscous flows in external flow fields is described in this paper. The model, based on transient Navier,Stokes equations, can solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the projection method. The pressure is assumed to be zero at infinite boundary and the external flow field is simulated using a direct boundary element method (BEM) by solving a pressure Poisson equation. A three-step finite element method (FEM) is used to solve the momentum equations of the flow. The present model is applied to simulate high-Reynolds number flow past a single circular cylinder and flow past two cylinders in which one acts as a control cylinder. The simulation results are compared with experimental data and other numerical models and are found to be feasible and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||