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Pressure Correction (pressure + correction)

Distribution by Scientific Domains
Engineering85%

Selected Abstracts

A control volume finite-element method for numerical simulating incompressible fluid flows without pressure correction

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007
Ahmed Omri
Abstract This paper presents a numerical model to study the laminar flows induced in confined spaces by natural convection. A control volume finite-element method (CVFEM) with equal-order meshing is employed to discretize the governing equations in the pressure,velocity formulation. In the proposed model, unknown variables are calculated in the same grid system using different specific interpolation functions without pressure correction. To manage memory storage requirements, a data storage format is developed for generated sparse banded matrices. The performance of various Krylov techniques, including Bi-CGSTAB (Bi-Conjugate Gradient STABilized) with an incomplete LU (ILU) factorization preconditioner is verified by applying it to three well-known test problems. The results are compared to those of independent numerical or theoretical solutions in literature. The iterative computer procedure is improved by using a coupled strategy, which consists of solving simultaneously the momentum and the continuity equation transformed in a pressure equation. Results show that the strategy provides useful benefits with respect to both reduction of storage requirements and central processing unit runtime. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Further experiences with computing non-hydrostatic free-surface flows involving water waves

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005
Marcel Zijlema
Abstract A semi-implicit, staggered finite volume technique for non-hydrostatic, free-surface flow governed by the incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time. The procedure is intended to be used for predicting wave propagation in coastal areas. The splitting of the pressure into hydrostatic and non-hydrostatic components is utilized. To ease the task of discretization and to enhance the accuracy of the scheme, a vertical boundary-fitted co-ordinate system is employed, permitting more resolution near the bottom as well as near the free surface. The issue of the implementation of boundary conditions is addressed. As recently proposed by the present authors, the Keller-box scheme for accurate approximation of frequency wave dispersion requiring a limited vertical resolution is incorporated. The both locally and globally mass conserved solution is achieved with the aid of a projection method in the discrete sense. An efficient preconditioned Krylov subspace technique to solve the discretized Poisson equation for pressure correction with an unsymmetric matrix is treated. Some numerical experiments to show the accuracy, robustness and efficiency of the proposed method are presented. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A high-order finite difference method for incompressible fluid turbulence simulations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003
Eric Vedy
Abstract A Hermitian,Fourier numerical method for solving the Navier,Stokes equations with one non-homogeneous direction had been presented by Schiestel and Viazzo (Internat. J. Comput. Fluids 1995; 24(6):739). In the present paper, an extension of the method is devised for solving problems with two non-homogeneous directions. This extension is indeed not trivial since new algorithms will be necessary, in particular for pressure calculation. The method uses Hermitian finite differences in the non-periodic directions whereas Fourier pseudo-spectral developments are used in the remaining periodic direction. Pressure,velocity coupling is solved by a simplified Poisson equation for the pressure correction using direct method of solution that preserves Hermitian accuracy for pressure. The turbulent flow after a backward facing step has been used as a test case to show the capabilities of the method. The applications in view are mainly concerning the numerical simulation of turbulent and transitional flows. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Flows through horizontal channels of porous materials

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 10 2003
A.K. Al-Hadhrami
Abstract In this paper, the control volume method (CVM) with the staggered grid system is utilized to solve the two-dimensional Brinkman equation for different configurations of porous media in a horizontal channel. The values of the permeability of sand and clear fluid are considered when performing several numerical investigations which enable the evaluation of the behaviour of the flow through regions that mathematically model some geological features (faults/fractures) present in oil reservoirs or groundwater flows. We have found that the convergence of the CVM can be achieved within a reasonable number of iterations when there is a gap present between a partial barrier of low Darcy number and the channel boundary. However, a complete barrier across the channel results in a very high resistance and hence there is a large pressure drop which causes difficulties in convergence. In order to improve the rate of convergence in such situations, an average pressure correction (APC) technique, which is based on global mass conservation, is developed. The use of this technique, along with the CVM, can rapidly build up the pressure drop across such a barrier and hence dramatically improve the rate of convergence of the iterative scheme. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Fountain flow revisited: The effect of various fluid mechanics parameters

AICHE JOURNAL, Issue 5 2010
Evan Mitsoulis
Abstract Numerical simulations have been undertaken for the benchmark problem of fountain flow present in injection-mold filling. The finite element method (FEM) is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal, steady-state conditions for Newtonian fluids. The effects of inertia, gravity, surface tension, compressibility, slip at the wall, and pressure dependence of the viscosity are all considered individually in parametric studies covering a wide range of the relevant parameters. These results extend previous ones regarding the shape of the front, and in particular the centerline front position, as a function of the dimensionless parameters. The pressures from the simulations have been used to compute the excess pressure losses in the system (front pressure correction or exit correction). Inertia leads to highly extended front positions relative to the inertialess Newtonian values, which are 0.895 for the planar case and 0.835 for the axisymmetric one. Gravity acting in the direction of flow shows the same effect, while gravity opposing the flow gives a reduced bulge of the fountain. Surface tension, slip at the wall, and compressibility, all decrease the shape of the front. Pressure-dependence of the viscosity leads to increased front position as a corresponding dimensionless parameter goes from zero (no effect) to higher values of the pressure-shift factor. The exit correction increases monotonically with inertia, compressibility, and gravity, while it decreases monotonically with slip and pressure-dependence of the viscosity. Contour plots of the primary variables (velocity-pressure) show interesting trends compared with the base case (zero values of the dimensionless parameters and of surface tension). © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

A collocated, iterative fractional-step method for incompressible large eddy simulation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
Giridhar Jothiprasad
Abstract Fractional-step methods are commonly used for the time-accurate solution of incompressible Navier,Stokes (NS) equations. In this paper, a popular fractional-step method that uses pressure corrections in the projection step and its iterative variants are investigated using block-matrix analysis and an improved algorithm with reduced computational cost is developed. Since the governing equations for large eddy simulation (LES) using linear eddy-viscosity-based sub-grid models are similar in form to the incompressible NS equations, the improved algorithm is implemented in a parallel LES solver. A collocated grid layout is preferred for ease of extension to curvilinear grids. The analyzed fractional-step methods are viewed as an iterative approximation to a temporally second-order discretization. At each iteration, a linear system that has an easier block-LU decomposition compared with the original system is inverted. In order to improve the numerical efficiency and parallel performance, modified ADI sub-iterations are used in the velocity step of each iteration. Block-matrix analysis is first used to determine the number of iterations required to reduce the iterative error to the discretization error of. Next, the computational cost is reduced through the use of a reduced stencil for the pressure Poisson equation (PPE). Energy-conserving, spatially fourth-order discretizations result in a 7-point stencil in each direction for the PPE. A smaller 5-point stencil is achieved by using a second-order spatial discretization for the pressure gradient operator correcting the volume fluxes. This is shown not to reduce the spatial accuracy of the scheme, and a fourth-order continuity equation is still satisfied to machine precision. The above results are verified in three flow problems including LES of a temporal mixing layer. Copyright © 2008 John Wiley & Sons, Ltd. [source]