An accurate shock-capturing scheme based on rotated-hybrid Riemann solver

2016 ◽  
Vol 26 (5) ◽  
pp. 1310-1327 ◽  
Author(s):  
Ghislain Tchuen ◽  
Pascalin Tiam Kapen ◽  
Yves Burtschell
Keyword(s):  
Compressible Flow ◽  
Finite Volume ◽  
Compressible Flows ◽  
Navier Stokes ◽  
Shock Propagation ◽  
Riemann Solver ◽  
Simple Task ◽  
Content Type ◽  
Flow Problems ◽  
Roe Solver

Purpose – The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Design/methodology/approach – The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task. Findings – The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods. Practical implications – The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Originality/value – The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

An Advanced Unstructured-Grid Finite-Volume Design System for Gas Turbine Combustion Analysis

2013 ◽  
Author(s):  
M. S. Anand ◽  
R. Eggels ◽  
M. Staufer ◽  
M. Zedda ◽  
J. Zhu
Keyword(s):  
Finite Volume ◽  
Compressible Flows ◽  
Turbulence Models ◽  
General Purpose ◽  
Navier Stokes ◽  
Design System ◽  
Analysis Tool ◽  
Combustion Chemistry ◽  
Finite Volume Approach ◽  
Complicated Geometries

A general-purpose combustion Computational Fluid Dynamics (CFD) design analysis tool has been developed. The method is pressure-based and applicable to both incompressible and compressible flows. The unstructured finite-volume approach used can take arbitrary shapes of mesh cells to resolve complicated geometries. Turbulence is simulated either by Reynolds-Averaged Navier-Stokes (RANS) or by Large Eddy Simulation (LES) approaches. Combustion is modeled by various combinations of combustion chemistry and combustion-turbulence models including transport probability density function (PDF) model. A Lagrangian approach is used to simulate fuel spray droplet. The resulting tool has being used in routine combustor simulations for a variety of commercial and military combustor development programs. Application examples presented include simulations of several combustors and comparisons with available rig data.

Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbomachinery Applications

2014 ◽  
Author(s):  
Luca Mangani ◽  
Marwan Darwish ◽  
Fadl Moukalled
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Computational Cost ◽  
Simple Algorithm ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Analysis And Design ◽  
Flow Problems ◽  
Matrix Coefficients

In this paper we present a fully coupled algorithm for the resolution of compressible flows at all speed. The pressure-velocity coupling at the heart of the Navier Stokes equations is accomplished by deriving a pressure equation in similar fashion to what is done in the segregated SIMPLE algorithm except that the influence of the velocity fields is treated implicitly. In a similar way, the assembly of the momentum equations is modified to treat the pressure gradient implicitly. The resulting extended system of equations, now formed of matrix coefficients that couples the momentum and pressure equations, is solved using an algebraic multigrid solver. The performance of the coupled approach and the improved efficiency of the novel developed code was validated comparing results with experimental and numerical data available from reference literature test cases as well as with segregated solver as exemplified by the SIMPLE algorithm. Moreover the reference geometries considered in the validation process cover the typical aerodynamics applications in gas turbine analysis and design, considering Euler to turbulent flow problems and clearly indicating the substantial improvements in terms of computational cost and robustness.

Quick finite volume solver for incompressible Navier-Stokes equation by parallel Gram-Schmidt process based GMRES and HSS

2015 ◽  
Vol 32 (5) ◽  
pp. 1460-1476
Author(s):  
Di Zhao
Keyword(s):  
Linear System ◽  
Saddle Point ◽  
Stokes Equation ◽  
Finite Volume ◽  
Saddle Point Problem ◽  
Navier Stokes ◽  
Point Problem ◽  
Navier Stokes Equation ◽  
Content Type ◽  
Incompressible Navier Stokes Equation

Purpose – The purpose of this paper is to develop Triple Finite Volume Method (tFVM), the author discretizes incompressible Navier-Stokes equation by tFVM, which leads to a special linear system of saddle point problem, and most computational efforts for solving the linear system are invested on the linear solver GMRES. Design/methodology/approach – In this paper, by recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS) and the parallel implementation of GMRES, the author develops a quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation. Findings – Computational results show that, the quick solver HSS-pGMRES-tFVM significantly increases the solution speed for saddle point problem from incompressible Navier-Stokes equation than the conventional solvers. Originality/value – Altogether, the contribution of this paper is that the author developed the quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

A Finite Volume Chimera Method for Fast Transient Dynamics in Compressible Flow Problems

2021 ◽  
pp. 1-27
Author(s):  
Alexis Picard ◽  
Nicolas Lelong ◽  
Olivier Jamond ◽  
Vincent Faucher ◽  
Christian Tenaud
Keyword(s):  
Compressible Flow ◽  
Finite Volume ◽  
Transient Dynamics ◽  
Flow Problems ◽  
Fast Transient

Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem

2016 ◽  
Vol 26 (8) ◽  
pp. 2462-2485 ◽  
Author(s):  
Juan Wen ◽  
Yinnian He ◽  
Xin Zhao
Keyword(s):  
Finite Volume ◽  
Stokes Problem ◽  
Volume Element ◽  
New Method ◽  
Navier Stokes ◽  
Optimal Order ◽  
Finite Volume Element Method ◽  
Content Type ◽  
Finite Volume Element ◽  
Element Method

Purpose The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem. Design/methodology/approach This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P1/P1. Findings The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained. Originality/value Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.

scholarly journals Implementation of the Compressible Flow Solution Methodology for Solving 2D Shallow-Water Flow Problems

2001 ◽  
Author(s):  
Joaquin E. Moran ◽  
Jose A. Rincon
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Compressible Flow ◽  
Water Flow ◽  
Compressible Flows ◽  
Shallow Water Flow ◽  
Pressure Correction ◽  
Flow Solution ◽  
Flow Problems ◽  
Solution Methodology

Abstract This paper concerns with the implementation of the compressible flow solution methodology for solving 2D shallow water flow problems. It is well known that in both cases, the continuity and momentum conservation equations look quite similar, but depth replaces density of compressible flow, and the Froude number will replace the Mach number. Thus, any mass imbalance produces a change in depth equivalent to the density change for compressible flow. It is possible to combine momentum and continuity equations to obtain a predictor-corrector algorithm for establishing the depth field. However, as the Froude number increases, the governing equations change their character from elliptic to hyperbolic, with a parabolic transition at a Froude number of unity and this change is not reflected in the equivalent classical pressure-correction equation, which keeps its elliptic character. The extension of incompressible (SIMPLE-based methods) to compressible flows, incorporates a convection-like term (wave velocity related) to the pressure-correction equation. The drawback of the extension of the pressure-correction to compressible flows was the poor shock-capturing capability, which is due mainly to the treatment of the convective terms in the conservation equations. In this work, a high order bounded treatment of the convective terms along with the depth-correction for all Froude numbers is implemented. A numerical solution is presented for all Froude numbers, and it is compared with benchmark problems.

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