scholarly journals A mimetic numerical scheme for multi-fluid flows with thermodynamic and geometric compatibility on an arbitrarily moving grid

2020 ◽  
Vol 132 ◽  
pp. 103324
Author(s):  
Thibaud Vazquez-Gonzalez ◽  
Antoine Llor ◽  
Christophe Fochesato
Keyword(s):  
Numerical Scheme ◽  
Fluid Flows ◽  
Moving Grid ◽  
Geometric Compatibility

scholarly journals A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles

2014 ◽  
Vol 24 (10) ◽  
pp. 2043-2083 ◽  
Author(s):  
Frédéric Coquel ◽  
Khaled Saleh ◽  
Nicolas Seguin
Keyword(s):  
Cross Section ◽  
Gas Dynamics ◽  
Numerical Scheme ◽  
Fluid Flows ◽  
Finite Volume Scheme ◽  
Riemann Solver ◽  
Time Step ◽  
Piecewise Constant ◽  
Entropy Satisfying ◽  
Do So

We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the cross-section and on an approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme for all variation of section, even discontinuous sections with arbitrary large jumps. To do so, we introduce, in the first step of the relaxation solver, a singular dissipation measure superposed on the standing wave, which enables us to control the approximate speeds of sound and thus the time step, even for extreme initial data.

scholarly journals Computation of 3D Water Flows by the Double Potential Method for the Simulation of Electromagnetic Water Purification

2020 ◽  
Vol 226 ◽  
pp. 02021 ◽  
Author(s):  
Nikita Tarasov ◽  
Sergey Polyakov ◽  
Tatiana Kudryashova
Keyword(s):  
Water Purification ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Potential Method ◽  
Software Implementation ◽  
Three Dimensional Flow ◽  
Exponential Transformation ◽  
Water Flows ◽  
Volume Method

In this paper, we discuss the modeling of the electromagnetic water purification. This model requires a velocity distribution in a study domain. For that purpose, the double potential method for simulating incompressible viscous fluid flows was used. The system of equations was discretized with the help of the finite volume method using an exponential transformation for the vortex calculation. As a result, a software implementation of the developed numerical scheme was obtained. The simulation of the three-dimensional flow was carried out in a study domain. The results were compared with Ansys CFD. The comparison showed a good degree of consistency between the two distributions. Using the obtained velocity field, we simulated the process of water purification using the induction of the electromagnetic field.

Macroscopic Streamline Integral Relations for Two-Phase Flows

1975 ◽  
Vol 42 (4) ◽  
pp. 766-770 ◽  
Author(s):  
D. A. Drew
Keyword(s):  
Pressure Drop ◽  
Numerical Scheme ◽  
Flow Model ◽  
Fluid Flows ◽  
Phase Flow ◽  
Two Phase ◽  
Nonuniform Fluid ◽  
Flow Through ◽  
Net Flux ◽  
Integral Relations

A spout-fluidized bed is an example of a situation where a nonuniform fluid flow through a bed of particles causes particle circulation. Several integral relations are derived from a steady, two-dimensional two-phase flow model. The vorticity of the particle motion enclosed by a particle streamline is shown to be equal to the fluid vorticity enclosed by that streamline. The net flux of fluid vorticity through a particle streamline is shown to be equal to zero. The pressure drop along a fluid streamline is related to the net drag force along that streamline. The net flux of particle vorticity through a fluid streamline is given in terms of the pressure drop. Implications of these relations to the mechanics of particle-fluid flows are discussed. Relations giving the particle vorticity in terms of an integral of the fluid vorticity, and vice versa, are presented. A possible numerical scheme for calculation of the flow fields is discussed.

scholarly journals A NUMERICAL SCHEME FOR SOLVING CREEPING FLOWS

2003 ◽  
Vol 2 (2) ◽  
Author(s):  
H. A. Navarro ◽  
V. G. Ferreira
Keyword(s):  
Numerical Scheme ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Creeping Flows ◽  
Adi Schemes ◽  
Adi Scheme

This work shows an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows at low Reynolds numbers. The conservation equations are solved in stream function - vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient to simulate a creeping flow. Numerical results demonstrating the applicability of this technique are also presented.

Finite Analytic Method for 2D Fluid Flows in Porous Media with Full Tensor Permeability

2014 ◽  
Vol 668-669 ◽  
pp. 181-184
Author(s):  
Zhi Fan Liu
Keyword(s):  
Porous Media ◽  
Numerical Scheme ◽  
Fluid Flows ◽  
Heterogeneous Porous Media ◽  
Convergence Speed ◽  
Analytic Method ◽  
Permeability Heterogeneity ◽  
Finite Analytic Method ◽  
Traditional Scheme ◽  
Tensor Permeability

In this paper, the finite analytic method is developed to solve the two-dimensional fluid flows in heterogeneous porous media with full tensor permeability. With the help of power-law behaviors of pressure and its gradient around the node, a local analytic nodal solution is derived for the pressure equation. Then it is applied to construct a finite analytic numerical scheme which deals with the divergence in pressure gradient. The numerical examples show that the convergence speed of the numerical scheme is fast and independent of the permeability heterogeneity. In contrast, the convergence speed slow rapidly as the heterogeneity increases when the traditional scheme is used.

scholarly journals A NUMERICAL SCHEME FOR SOLVING CREEPING FLOWS

2003 ◽  
Vol 2 (2) ◽  
pp. 35
Author(s):  
H. A. Navarro ◽  
V. G. Ferreira
Keyword(s):  
Numerical Scheme ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Creeping Flows ◽  
Adi Schemes ◽  
Adi Scheme

This work shows an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows at low Reynolds numbers. The conservation equations are solved in stream function - vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient to simulate a creeping flow. Numerical results demonstrating the applicability of this technique are also presented.

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