Home About us Contact
|
Home About us Contact | ||
|
|
||
Pressure Equation (pressure + equation)
Selected AbstractsAn analysis and comparison of the time accuracy of fractional-step methods for the Navier,Stokes equations on staggered gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2002S. Armfield Abstract Fractional-step methods solve the unsteady Navier,Stokes equations in a segregated manner, and can be implemented with only a single solution of the momentum/pressure equations being obtained at each time step, or with the momentum/pressure system being iterated until a convergence criterion is attained. The time accuracy of such methods can be determined by the accuracy of the momentum/pressure coupling, irrespective of the accuracy to which the momentum equations are solved. It is shown that the time accuracy of the basic projection method is first-order as a result of the momentum/pressure coupling, but that by modifying the coupling directly, or by modifying the intermediate velocity boundary conditions, it is possible to recover second-order behaviour. It is also shown that pressure correction methods, implemented in non-iterative or iterative form and without special boundary conditions, are second-order in time, and that a form of the non-iterative pressure correction method is the most efficient for the problems considered. Copyright © 2002 John Wiley & Sons, Ltd. [source] Accelerating iterative solution methods using reduced-order models as solution predictorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006R. Markovinovi Abstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source] Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Dong-Liang Sun Abstract Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9,52.7% over SIMPLER algorithm, by 45.3,73.4% over SIMPLEC algorithm and by 10.7,53.1% over PISO algorithm. Copyright © 2009 John Wiley & Sons, Ltd. [source] Positive-definite q -families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Michael G. Edwards Abstract A new family of locally conservative cell-centred flux-continuous schemes is presented for solving the porous media general-tensor pressure equation. A general geometry-permeability tensor approximation is introduced that is piecewise constant over the subcells of the control volumes and ensures that the local discrete general tensor is elliptic. A family of control-volume distributed subcell flux-continuous schemes are defined in terms of the quadrature parametrization q (Multigrid Methods. Birkhauser: Basel, 1993; Proceedings of the 4th European Conference on the Mathematics of Oil Recovery, Norway, June 1994; Comput. Geosci. 1998; 2:259,290), where the local position of flux continuity defines the quadrature point and each particular scheme. The subcell tensor approximation ensures that a symmetric positive-definite (SPD) discretization matrix is obtained for the base member (q=1) of the formulation. The physical-space schemes are shown to be non-symmetric for general quadrilateral cells. Conditions for discrete ellipticity of the non-symmetric schemes are derived with respect to the local symmetric part of the tensor. The relationship with the mixed finite element method is given for both the physical-space and subcell-space q -families of schemes. M -matrix monotonicity conditions for these schemes are summarized. A numerical convergence study of the schemes shows that while the physical-space schemes are the most accurate, the subcell tensor approximation reduces solution errors when compared with earlier cell-wise constant tensor schemes and that subcell tensor approximation using the control-volume face geometry yields the best SPD scheme results. A particular quadrature point is found to improve numerical convergence of the subcell schemes for the cases tested. Copyright © 2007 John Wiley & Sons, Ltd. [source] A control volume finite-element method for numerical simulating incompressible fluid flows without pressure correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Ahmed 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] Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Mayur Pal Abstract In this paper, a numerical convergence study of family of flux-continuous schemes is presented. The family of flux-continuous schemes is characterized in terms of quadrature parameterization, where the local position of continuity defines the quadrature point and hence the family. A convergence study is carried out for the discretization in physical space and the effect of a range of quadrature points on convergence is explored. Structured cell-centred and unstructured cell-vertex schemes are considered. Homogeneous and heterogeneous cases are tested, and convergence is established for a number of examples with discontinuous permeability tensor including a velocity field with singularity. Such cases frequently arise in subsurface flow modelling. A convergence comparison with CVFE is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Analysis of incompressible miscible displacement in porous media by characteristics collocation methodNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2006Ning Ma Abstract Miscible displacement of one incompressible fluid by another in a porous medium is modelled by a coupled system of two partial differential equations. The pressure equation is elliptic, whereas the concentration equation is parabolic but normally convection-dominated. In this article, the collocation scheme is used to approximate the pressure equation and another characteristics collocation scheme to treat concentration equation. Existence and uniqueness of solutions of the algorithm are proved. Optimal order error estimate is demonstrated. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source] On the convergence of the multi-point flux approximation O-method: Numerical experiments for discontinuous permeabilityNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2005G. T. Eigestad Abstract This article presents numerical convergence results for the multi-point flux approximation (MPFA) O-method applied to the pressure equation in 2D. The discretization is made directly in physical space, and the investigated cases are simulated on structured, but generally skew grids. Skew grids need to be used to correctly represent the physics of the underlying flow problems. Special emphasis is made on cases which impose singularities in the velocity field. Such cases frequently arise in the description of subsurface flow. Analytical tools may not be applicable to fully answer the question of convergence for such cases; in particular not for the physical space discretization. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source] A splitting positive definite mixed element method for miscible displacement of compressible flow in porous mediaNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2001Danping Yang Abstract A miscible displacement of one compressible fluid by another in a porous medium is governed by a nonlinear parabolic system. A new mixed finite element method, in which the mixed element system is symmetric positive definite and the flux equation is separated from pressure equation, is introduced to solve the pressure equation of parabolic type, and a standard Galerkin method is used to treat the convection-diffusion equation of concentration of one of the fluids. The convergence of the approximate solution with an optimal accuracy in L2 -norm is proved. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 229,249, 2001 [source] An implicit edge-based ALE method for the incompressible Navier,Stokes equations,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003Richard W. Smith Abstract A new finite volume method for the incompressible Navier,Stokes equations, expressed in arbitrary Lagrangian,Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is first evaluated using several well-known unsteady incompressible Navier,Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in 2003 by John Wiley & Sons, Ltd. [source] | ||||||||||