# Numerical schemes in PHOENICS code

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 July 31, 2000, 10:00 Numerical schemes in PHOENICS code #1 Hafsia Guest   Posts: n/a The Non linear convection and Crank Nickolson schemes, implemented in the PHOENICS code, are activated by source term associated to a transport variable other than the velocity components. How the discretized momentum equations are modified by this activation procedure ? Thank you. Hydraulic and Environemental Modeling Laboratory National Engineering School of Tunisia

 July 31, 2000, 11:45 Re: Numerical schemes in PHOENICS code #2 Mike Malin Guest   Posts: n/a The higher-order numerical schemes embodied in PHOENICS are fully described in: http://www.simuserve.com/cfd-shop/vol12-2.htm#malin The document includes a description of the finite-volume analogues of the convection terms along with their implementation in the PHOENICS GX routines. Mike Malin

 September 11, 2000, 19:16 Re: Numerical schemes in PHOENICS code #3 clifford bradford Guest   Posts: n/a is phoenics a coupled or uncoupled solver?

 September 12, 2000, 04:26 Re: Numerical schemes in PHOENICS code #4 Mike Malin Guest   Posts: n/a I am not sure what you precisely mean, but I presume that you are referring to the velocity-pressure coupling in the numerical solution procedure. The default in PHOENICS is to use uncoupling, but for single-phase flows an option is now available to carry out the solution with a coupled solver.

 September 12, 2000, 15:28 Re: Numerical schemes in PHOENICS code #5 clifford bradford Guest   Posts: n/a What I mean is it a pressure based ie uncoupled (SIMPLE PISO etc) or is it a time iterative scheme ie coupled (Crank-nicholson, runge-kutta etc). also what spatial differencing methods are employed

 September 13, 2000, 04:45 Re: Numerical schemes in PHOENICS code #6 Mike Malin Guest   Posts: n/a The default is to use uncoupled velocity-pressure coupling, i.e. to use segregated continuity and momentum equations and to solve in an iterative manner by means of the SIMPLEST algorithm, which is a variant of the pioneering SIMPLE method of Patankar and Spalding. Time-marching to a steady-state by use of SIMPLEST is permitted as an alternative to repeated sweeps of the solution domain. For single-phase flows, an option exists to solve the continuity and momentum equations simultaneously by means of an algebraic nulti-grid solver. Specifically, PHOENICS 2.2 and later releases provide for 5 alternative linear schemes, and 12 alternative non-linear schemes. The linear schemes are based on the Kappa formulation, and comprise CDS, QUICK, the cubic upwind scheme (CUS), the linear upwind scheme (LUS) and Fromm's scheme. The non-linear schemes extend the Kappa formulation so as to employ a flux limiter to secure boundedness at the expense of reduced accuracy. The non-linear schemes currently available are: SMART, H-QUICK, UMIST, Koren, Superbee, Minmod, OSPRE, van Albada, MUSCL, CHARM, H-CUS and van-Leer harmonic. All these schemes are documented in the reference cited in my message of 31/07/00.

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