Solutions of High-order Methods for Three-dimensional Compressible Viscous Flows

2012 ◽  
Author(s):  
Li Wang ◽  
W Kyle Anderson ◽  
Jon Erwin
Keyword(s):  
Three Dimensional ◽  
Viscous Flows ◽  
High Order ◽  
High Order Methods ◽  
Compressible Viscous Flows

High-Order Methods for Three-Dimensional Strand-Cartesian Grids

2015 ◽  
Author(s):  
Oisin Tong ◽  
Aaron J. Katz ◽  
Andrew M. Wissink ◽  
Jayanarayanan Sitaraman
Keyword(s):  
Three Dimensional ◽  
High Order ◽  
Cartesian Grids ◽  
High Order Methods

A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh

2015 ◽  
Vol 17 (3) ◽  
pp. 615-656 ◽  
Author(s):  
Marc R. J. Charest ◽  
Clinton P. T. Groth ◽  
Pierre Q. Gauthier
Keyword(s):  
Finite Volume ◽  
Unstructured Mesh ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Unstructured Meshes ◽  
High Order ◽  
Finite Volume Scheme ◽  
Low Speed ◽  
Volume Scheme

AbstractHigh-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

Study of Viscous Flows Using High-Order Methods and Curved Boundary Treatment

2017 ◽  
Author(s):  
André Ribeiro de Barros Aguiar ◽  
Fábio Mallaco Moreira ◽  
Eduardo Jourdan ◽  
João Luiz F. Azevedo
Keyword(s):  
Viscous Flows ◽  
High Order ◽  
High Order Methods ◽  
Curved Boundary ◽  
Boundary Treatment

Comparison of two methods for solving three-dimensional unsteady compressible viscous flows

AIAA Journal ◽  
1994 ◽  
Vol 32 (10) ◽  
pp. 1978-1984 ◽  
Author(s):  
Ray Hixon ◽  
Fu-Lin Tsung ◽  
L. N. Sankar
Keyword(s):  
Three Dimensional ◽  
Viscous Flows ◽  
Compressible Viscous Flows

A generalized sphere function-based gas kinetic scheme for simulation of compressible viscous flows

2020 ◽  
Vol 34 (14n16) ◽  
pp. 2040079
Author(s):  
Tian-Peng Yang ◽  
Jiang-Feng Wang
Keyword(s):  
Distribution Function ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Kinetic Scheme ◽  
Viscous Flows ◽  
Dimensional Case ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Present Scheme ◽  
Compressible Viscous Flows

In this paper, a generalized sphere function-based gas kinetic scheme (GKS) is developed for simulation of two-dimensional compressible viscous flows. This work aims to improve the existing simplified GKS, in which a simple two-dimensional/three-dimensional distribution function is used as the equilibrium state. The present scheme applies the finite volume method to discretize Navier–Stokes equations and the numerical flux at cell interface is evaluated by the local reconstruction of solution for the continuous Boltzmann equation with [Formula: see text]-dimensional sphere function. This local solution contains both the equilibrium part and nonequilibrium part, and the contribution of the nonequilibrium part is controlled by a switch function. It is found that the present scheme has the same expression as the circular function-based GKS for the two-dimensional case and the sphere function-based GKS for the three-dimensional case. Therefore, these two GKSs can be unified, and the developed method provides another way for the simple distribution function.

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