A splitting method for the isentropic Baer-Nunziato two-phase flow model (original) (raw)

Numerical approximation for a Baer–Nunziato model of two-phase flows

Applied Numerical Mathematics, 2011

We present a well-balanced numerical scheme for approximating the solution of the Baer-Nunziato model of two-phase flows by balancing the source terms and discretizing the compaction dynamics equation. First, the system is transformed into a new one of three subsystems: the first subsystem consists of the balance laws in the gas phase, the second subsystem consists of the conservation law of the mass in the solid phase and the conservation law of the momentum of the mixture, and the compaction dynamic equation is considered as the third subsystem. In the first subsystem, stationary waves are used to build up a well-balanced scheme which can capture equilibrium states. The second subsystem is of conservative form and thus can be numerically treated in a standard way. For the third subsystem, the fact that the solid velocity is constant across the solid contact suggests us to compose the technique of the Engquist-Osher scheme. We show that our scheme is capable of capturing exactly equilibrium states. Moreover, numerical tests show the convergence of approximate solutions to the exact solution.

A fractional-step method for steady-state flow

Journal of Computational Physics, 2019

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

New approximate analytical technique for the solution of time fractional fluid flow models

Advances in Difference Equations

In this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier–Stokes model. The approximate analytical solution is obtained within Liouville–Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology.

Accuracy of the operator splitting technique for two-phase flow with stiff source terms

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

Studying the Numerical Methods for Calculating Bi-Phase Fluid Flow

In calculations of shipbuilding and reviewing the marine phenomena, numerical solution of bi-phase fluid plays a major role. So many researches are conducted in the sea, lakes, and canals. Numerical solution of this flow is presented by Navier-Stokes, continuity and surface fitted equations. Based on the bi-phase physical properties of flow requiring discretion of governing equations coupling above equations is important. In this paper, distribution of bi-phase fluid is obtained in the whole range of calculation by solving the surface fitted equations by interface capturing method. Therefore, equations governing on the fluid flow will be solved for a bi-phase fluid. For coupling the velocity and pressure field, " fractional step method " was also used. Apparently, the only wise selection in any part of numerical solution algorithm-together with dominance on existing selections conformed to the requirements of problems ahead-resulted in developing an efficient numerical method that is the basis for this paper aiming to provide a platform for this issue.

Numerical solutions for fractional reaction–diffusion equations

Computers & Mathematics with Applications, 2008

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fractional derivative used. Fractional reaction-diffusion equations combine the fractional diffusion with a classical reaction term. In this paper, we develop a practical method for numerical solution of fractional reactiondiffusion equations, based on operator splitting. Then we present results of numerical simulations to illustrate the method, and investigate properties of numerical solutions. We also discuss applications to biology, where the reaction term models species growth and the diffusion term accounts for movements.

Application of a fractional-step method to incompressible Navier-Stokes equations

Journal of Computational Physics, 1985

A numerical method for computing three-dimensional, time-dependent incompressible flows is presented. The method is based on a fractional-step, or time-splitting, scheme in conjunction with the approximate-factorization technique. It is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions. Appropriate boundary conditions for the intermediate velocity field are derived and tested. Numerical solutions for flows inside a driven cavity and over a backward-facing step are presented and compared with experimental data and other numerical results.

An approximate solution for a fractional diffusion-wave equation using the decomposition method

Applied Mathematics and Computation, 2005

The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order a, 0 < a 6 2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the Caputo sense. Numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process (a = 1) to a pure wave process (a = 2).

Approximate solutions of the Baer-Nunziato Model

2013

We examine in this paper the accuracy of some approximations of the Baer-Nunziato two-phase flow model. The governing equations and their main properties are recalled, and two distinct numerical schemes are investigated, including a classical secondorder extension relying on symmetrizing variables. Shock tube cases are considered, and two simple Riemann problems based on well-balanced initial data are detailed. These enable to recover the expected convergence rates. However, it is shown that these simple cases are indeed very difficult and that the accuracy of basic schemes is rather poor.

Computation of solution to fractional order partial reaction diffusion equations

Journal of Advanced Research, 2020

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.