Numerical solution of Navier-Stokes equations for two-dimensional viscous compressible flows

AIAA Journal ◽  
1989 ◽  
Vol 27 (7) ◽  
pp. 843-844 ◽  
Author(s):  
Sunil Kumar Chakrabartty
Keyword(s):  
Numerical Solution ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Viscous Compressible Flows

DOMAIN DECOMPOSITION APPROXIMATION TO A GENERALIZED STOKES PROBLEM BY SPECTRAL METHODS

1991 ◽  
Vol 01 (04) ◽  
pp. 501-515 ◽  
Author(s):  
CLAUDIO CARLENZOLI ◽  
PAOLA ZANOLLI
Keyword(s):  
Spectral Methods ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Generalized Stokes Problem ◽  
Spectral Approximations ◽  
Viscous Compressible Flows

We consider here the approximation of a generalized Stokes problem by spectral methods in the collocation form. This problem is of particular interest when Navier-Stokes equations for viscous compressible flows are investigated. We also analyze a coupling of a viscous model with an inviscid one; precisely, we split the computational domain in two parts and in one of them we eliminate the viscous coefficient from the Stokes equations. Such an approach can be worthwhile in the study of compressible fluids around rigid profiles with critical layers. Finally we consider some numerical results with the aim of showing the excellent accuracy of the spectral approximations, as well as the efficiency of an iterative algorithm that we propose in order to alternate viscous and inviscid numerical solvers.

Numerical Simulation of the Two-Dimensional Viscous Compressible Flow in Blade Cascades Using a Solution-Adaptive Unstructured Mesh

1990 ◽  
Vol 112 (3) ◽  
pp. 311-319 ◽  
Author(s):  
G. L. D. Side´n ◽  
W. N. Dawes ◽  
P. J. Albra˚ten
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Rapid Development ◽  
Automatic Generation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Explicit Finite Element ◽  
Eddy Viscosity Model ◽  
Viscous Compressible Flow

An explicit finite element procedure has been coupled with an automatic generation procedure for mesh-adaptive steady-state simulations of two-dimensional viscous compressible flows in cascades. Turbulence is modeled by a two-layer algebraic eddy viscosity model. Results show good behavior in comparison with measurements and results of a conventional H-mesh viscous flow solver. Computed loss approaches measured loss as the mesh is refined. Currently, the unstructured solver suffers in efficiency terms because the automatic mesh generator tends to produce inefficient equilateral triangles in the regions of shock waves and boundary layers where stretched elements would be more appropriate. This means that, at least for the Navier–Stokes equations, the unstructured approach is not yet competitive with conventional structured techniques. Nevertheless, this will change once the key advantages of geometric flexibility and user-independent solutions force rapid development.

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

2016 ◽  
Vol 8 (6) ◽  
pp. 887-910 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Strong Shock ◽  
Viscous Flows ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Viscous Compressible Flows

AbstractIn this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

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