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Splitting Technique (splitting + technique)
Selected AbstractsSplit time-integration for low Mach number compressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2004H. C. de Lange Abstract In low-Mach number flows the time-integration is usually bounded by the stability of the acoustic fluxes. This poses a restriction to the maximum timestep. Integration of all fluxes on this time-scale, leads to huge cpu times. To decrease this problem a timestep splitting technique has been developed by which the acoustic, convective and diffusive fluxes are treated separately. The integration of each of the fluxes is bounded by their separate stability criteria. As an example, the time-integration technique will be applied to a temporally developing mixing layer. The results show that the proposed splitted integration technique, applied at a Mach number of 0.2, reduces the cpu time by about a factor three. Furthermore, it will be shown that the technique may also be applied at low (0.05) Mach number flows. Here, the cpu-reduction reaches its maximum of about a factor of four. Copyright © 2004 John Wiley & Sons, Ltd. [source] CBS versus GLS stabilization of the incompressible Navier,Stokes equations and the role of the time step as stabilization parameterINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2002R. Codina Abstract In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier,Stokes equations. The first is the characteristic-based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity,pressure interpolations. The second approach is the Galerkin-least-squares (GLS) method, in which a least-squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] A discrete splitting finite element method for numerical simulations of incompressible Navier,Stokes flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Kenn K. Q. Zhang Abstract The presence of the pressure and the convection terms in incompressible Navier,Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill-conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non-linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical simulation of one-dimensional flows through porous media with shock wavesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001Maria Laura Martins-Costa Abstract This work studies an unsaturated flow of a Newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and an inert gas (to account for the mixture compressibility). A set of two nonlinear partial differential equations describes the problem, which is approximated by means of a Glimm's scheme, combined with an operator splitting technique. Copyright © 2001 John Wiley & Sons, Ltd. [source] Linearized and non-linear acoustic/viscous splitting techniques for low Mach number flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Mohammad Farshchi Abstract Computation of the acoustic disturbances generated by unsteady low-speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two-step acoustic/viscous splitting technique. An optimized high order dispersion,relation,preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non-linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three-dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd. [source] An upwind finite volume scheme and its maximum-principle-preserving ADI splitting for unsteady-state advection-diffusion equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003Hong Wang Abstract We develop an upwind finite volume (UFV) scheme for unsteady-state advection-diffusion partial differential equations (PDEs) in multiple space dimensions. We apply an alternating direction implicit (ADI) splitting technique to accelerate the solution process of the numerical scheme. We investigate and analyze the reason why the conventional ADI splitting does not satisfy maximum principle in the context of advection-diffusion PDEs. Based on the analysis, we propose a new ADI splitting of the upwind finite volume scheme, the alternating-direction implicit, upwind finite volume (ADFV) scheme. We prove that both UFV and ADFV schemes satisfy maximum principle and are unconditionally stable. We also derive their error estimates. Numerical results are presented to observe the performance of these schemes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 211,226, 2003 [source] | ||||||||||