An approximate Riemann solver for real gas parabolized Navier–Stokes equations

2013 ◽  
Vol 233 ◽  
pp. 574-591 ◽  
Author(s):  
Annafederica Urbano ◽  
Francesco Nasuti
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Riemann Solver ◽  
Navier Stokes Equations ◽  
Real Gas ◽  
Approximate Riemann Solver

Unsteady Navier–Stokes Simulation of Transonic Cascade Flow Using an Unfactored Implicit Upwind Relaxation Scheme With Inner Iterations

1992 ◽  
Vol 114 (3) ◽  
pp. 599-606 ◽  
Author(s):  
M. Furukawa ◽  
T. Nakano ◽  
M. Inoue
Keyword(s):  
Stokes Equations ◽  
Unsteady Flows ◽  
Relaxation Method ◽  
Upwind Scheme ◽  
Navier Stokes ◽  
Riemann Solver ◽  
Approximate Factorization ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Approximate Riemann Solver

An implicit upwind scheme has been developed for Navier–Stokes simulations of unsteady flows in transonic cascades. The two-dimensional, Reynolds-averaged Navier–Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a highly accurate upwind scheme based on a TVD formulation with the Roe’s approximate Riemann solver, and the viscous fluxes are determined in a central differencing manner. The algebraic turbulence model of Baldwin and Lomax is employed. To simplify grid generations, a zonal approach with a composite zonal grid system is implemented, in which periodic boundaries are treated as zonal boundaries. A new time linearization of the inviscid fluxes evaluated by Roe’s approximate Riemann solver is presented in detail. No approximate factorization is introduced, and unfactored equations are solved by a pointwise relaxation method. To obtain time-accurate solutions, 30 linear iterations are performed at each time step. Numerical examples are presented for unsteady flows in a transonic turbine cascade where periodic unsteadiness is caused by the trailing edge vortex shedding.

scholarly journals Unsteady Navier-Stokes Simulation of Transonic Cascade Flow Using an Unfactored Implicit Upwind Relaxation Scheme With Inner Iterations

1991 ◽  
Author(s):  
M. Furukawa ◽  
T. Nakano ◽  
M. Inoue
Keyword(s):  
Stokes Equations ◽  
Unsteady Flows ◽  
Relaxation Method ◽  
Upwind Scheme ◽  
Navier Stokes ◽  
Riemann Solver ◽  
Approximate Factorization ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Approximate Riemann Solver

An implicit upwind scheme has been developed for Navier-Stokes simulations of unsteady flows in transonic cascades. The two-dimensional, Reynolds-averaged Navier-Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a highly accurate upwind scheme based on a TVD formulation with the Roe’s approximate Riemann solver, and the viscous fluxes are determined in a central differencing manner. The algebraic turbulence model of Baldwin and Lomax is employed. To simplify grid generations, a zonal approach with a composite zonal grid system is implemented, in which periodic boundaries are treated as zonal boundaries. A new time-linearization of the inviscid fluxes evaluated by the Roe’s approximate Riemann solver is presented in detail. No approximate factorization is introduced, and unfactored equations are solved by a pointwise relaxation method. To obtain time-accurate solutions, 30 inner iterations are performed at each time step. Numerical examples are presented for unsteady flows in a transonic turbine cascade where periodic unsteadiness is caused by the trailing edge vortex shedding.

scholarly journals Hydrodynamic Effects Produced by Submerged Breakwaters in a Coastal Area with a Curvilinear Shoreline

2019 ◽  
Vol 7 (10) ◽  
pp. 337 ◽  
Author(s):  
Francesco Gallerano ◽  
Giovanni Cannata ◽  
Federica Palleschi
Keyword(s):  
Coastal Area ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Integral Form ◽  
Navier Stokes ◽  
Hydrodynamic Effect ◽  
Riemann Solver ◽  
Three Dimensional Model ◽  
Navier Stokes Equations

A three-dimensional numerical study of the hydrodynamic effect produced by a system of submerged breakwaters in a coastal area with a curvilinear shoreline is proposed. The three-dimensional model is based on an integral contravariant formulation of the Navier-Stokes equations in a time-dependent curvilinear coordinate system. The integral form of the contravariant Navier-Stokes equations is numerically integrated by a finite-volume shock-capturing scheme which uses Monotonic Upwind Scheme for Conservation Laws Total Variation Diminishing (MUSCL-TVD) reconstructions and an Harten Lax van Leer Riemann solver (HLL Riemann solver). The numerical model is used to verify whether the presence of a submerged coastal defence structure, in the coastal area with a curvilinear shoreline, is able to modify the wave induced circulation pattern and the hydrodynamic conditions from erosive to accretive.

A strong conservative Riemann solver for the solution of the coupled Maxwell and Navier–Stokes equations

2014 ◽  
Vol 258 ◽  
pp. 431-450 ◽  
Author(s):  
Richard J. Thompson ◽  
Andrew Wilson ◽  
Trevor Moeller ◽  
Charles L. Merkle
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Riemann Solver ◽  
Navier Stokes Equations

Pressure over a dual-cavity cascade at supersonic speeds

1999 ◽  
Vol 103 (1019) ◽  
pp. 45-54 ◽  
Author(s):  
X. Zhang ◽  
J. A. Edwards
Keyword(s):  
Pressure Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Riemann Solver ◽  
Navier Stokes Equations ◽  
Pressure Drag ◽  
Pressure Distributions ◽  
Volume Algorithm ◽  
Cell Interface ◽  
Single Cavity

AbstractPressure distributions over a dual cavity cascade were studied at supersonic speeds of Mach 1·5 and 2·5. The study was performed through numerical modelling and results compared with model measurements. The Reynolds-averaged Navier-Stokes equations were solved using a finite-volume algorithm in which the inviscid cell interface fluxes were estimated using Roe's approximate Riemann solver with a second-order extension, and turbulence was modelled using a two-equationk-mmodel with compressibility corrections. Two test configurations were selected: (1) a length-to-depth ratioL/D =1 cavity followed by anotherL/D= 1 cavity, and (2) anL/D= 3 cavity followed by anL/D =1 cavity. The prediction was compared with that of a single cavity of the sameL/D.It was found that the pressure field around theL/D =1 cavity was substantially modified by a precedingL/D =3 cavity. Changes in the pressure and pressure drag coefficient were observed. The study clarified some earlier observations of unsteady modes over a dual cavity cascade, and confirmed model measurements of the pressure fluctuation under a number of flow and geometry conditions.

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