scholarly journals AN ENERGY DISSIPATIVE SPATIAL DISCRETIZATION FOR THE REGULARIZED COMPRESSIBLE NAVIER-STOKES-CAHN-HILLIARD SYSTEM OF EQUATIONS

2020 ◽  
Vol 25 (1) ◽  
pp. 110-129
Author(s):  
Vladislav Balashov ◽  
Alexander Zlotnik
Keyword(s):  
Body Force ◽  
Navier Stokes ◽  
Test Problems ◽  
Total Density ◽  
System Of Equations ◽  
Two Component ◽  
New Energy ◽  
Finite Difference Discretization ◽  
Parasitic Currents ◽  
Difference Discretization

We consider the regularized 3D Navier-Stokes-Cahn-Hilliard equations describing isothermal flows of viscous compressible two-component fluids with interphase effects. We construct for them a new energy dissipative finite-difference discretization in space, i.e., with the non-increasing total energy in time. This property is preserved in the absence of a regularization. In addition, the discretization is well-balanced for equilibrium flows and the potential body force. The sought total density, mixture velocity and concentration of one of the components are defined at nodes of one and the same grid. The results of computer simulation of several 2D test problems are presented. They demonstrate advantages of the constructed discretization including the absence of the so-called parasitic currents.

A New Method of Orthogonal Grid Generation

2011 ◽  
Vol 130-134 ◽  
pp. 757-760
Author(s):  
K. Ma ◽  
W.L. Wei
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Test Problems ◽  
Point Distribution ◽  
Good Balance ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for orthogonal grid generation is presented. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides is used. The proposed method is applied to various test problems£¬which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

Supercomputing of Supersonic Flows Using Upwind Relaxation and MacCormack Schemes

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
Oktay Baysal
Keyword(s):  
Stokes Equations ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Computational Algorithms ◽  
Navier Stokes Equations ◽  
Relaxation Scheme ◽  
Finite Volume Discretization ◽  
Finite Difference Discretization ◽  
The Mathematical Model ◽  
Difference Discretization

The impetus of this paper is the comparative applications of two numerical schemes for supersonic flows using computational algorithms tailored for a supercomputer. The mathematical model is the conservation form of Navier-Stokes equations with the effect of turbulence being modeled algebraically. The first scheme is an implicit, unfactored, upwind-biased, line-Gauss-Seidel relaxation scheme based on finite-volume discretization. The second scheme is the explicit-implicit MacCormack scheme based on finite-difference discretization. The best overall efficiences are obtained using the upwind relaxation scheme. The integrity of the solutions obtained for the example cases is shown by comparisons with experimental and other computational results.

Two-Dimensional Orthogonal Grid Generation

2012 ◽  
Vol 468-471 ◽  
pp. 2668-2671
Author(s):  
Y.L. Liu ◽  
K. Bai ◽  
Xi Wang ◽  
Ming Qin Liu
Keyword(s):  
Grid Generation ◽  
Test Problems ◽  
Two Dimensional ◽  
Point Distribution ◽  
Good Balance ◽  
Control Functions ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Generating System ◽  
Difference Discretization

A method for nearly orthogonal grid generation is presented in this study. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The grid quality control functions and grid properties are investigated. Specification of both boundary point distribution on all sides is used. The proposed method is applied to various test problems，which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

Research on Nearly Orthogonal Two-Dimensional Grid Generation

2011 ◽  
Vol 130-134 ◽  
pp. 2981-2984
Author(s):  
B.L. Su ◽  
W.L. Wei
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Moving Boundaries ◽  
Test Problems ◽  
Point Distribution ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for nearly orthogonal grid generation is presented in this study. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides and moving boundaries is used. The proposed method is applied to various test problems£¬which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

Research on Grid Generation

2012 ◽  
Vol 170-173 ◽  
pp. 3691-3694
Author(s):  
Y. L. Liu ◽  
Y. Bai ◽  
X.J. Zhao ◽  
W.L. Wei ◽  
K. Ma
Keyword(s):  
Control Function ◽  
Grid Generation ◽  
Test Problems ◽  
Point Distribution ◽  
Good Balance ◽  
Orthogonal Grid ◽  
Finite Difference Discretization ◽  
Grid Points ◽  
Generating System ◽  
Difference Discretization

A method for orthogonal grid generation is presented. The generating system is based on solution of a system of partial differential equations with finite difference discretization. The influence of the number of grid points, type of boundary, and intensity of the grid quality control function and grid properties are investigated. Specification of both boundary point distribution on all sides is used. The proposed method is applied to various test problems，which shows this method provides a good balance between controlling grid orthogonality and cell aspect ratio.

scholarly journals Two-component galaxy models with a central BH – II. The ellipsoidal case

2020 ◽  
Vol 500 (1) ◽  
pp. 1054-1070
Author(s):  
Luca Ciotti ◽  
Antonio Mancino ◽  
Silvia Pellegrini ◽  
Azadeh Ziaee Lorzad
Keyword(s):  
Dark Matter ◽  
Stellar Dynamics ◽  
Azimuthal Velocity ◽  
Dark Matter Halo ◽  
Gas Flows ◽  
Total Density ◽  
Density Distributions ◽  
Stellar Component ◽  
Two Component ◽  
Analytical Formulae

ABSTRACT Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

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