scholarly journals On Approximate Riemann Solvers within the Concept of the Unified Fractional-Step, Artificial Compressibility and Pressure Projection Method

2017 ◽  
Author(s):  
Kori Smith ◽  
Tom-Robin Teschner ◽  
László Könözsy
Keyword(s):  
Projection Method ◽  
Fractional Step ◽  
Riemann Solvers ◽  
Artificial Compressibility ◽  
Pressure Projection ◽  
Approximate Riemann Solvers

scholarly journals Implementation of the fractional-step, artificial compressibility with pressure projection (FSAC-PP) method into openfoam for unsteady flows

2021 ◽  
Vol 11 (5) ◽  
pp. 85-91
Author(s):  
Jesús Miguel Sánchez Gil ◽  
Tom-Robin Teschner ◽  
László Könözsy
Keyword(s):  
Time Derivative ◽  
Unsteady Flows ◽  
Time Discretization ◽  
Projection Methods ◽  
Fractional Step ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Start Up ◽  
2D Flow ◽  
Pressure Projection

Commercial and open-source CFD solvers rely mostly on incompressible approximate projection methods to overcome the pressure-velocity decoupling, such as the SIMPLE (Patankar, 1980) or PISO (Issa, 1986) algorithm. Incompressible methods based on the Artificial Compressibility method (Chorin, 1967) lack a mechanism to evolve in time and need to be supplemented by a real time derivative through the dual time scheme. The current study investigates the implementation of the explicit dual time discretization of the Artificial Compressibility method into OpenFOAM and extends on that by applying the dual time scheme to the incompressible FSAC-PP method (Könözsy, 2012). Applied to the Couette 2D flow at Re=100 and Re=1000, results show that for both methods accurate time evolutions of the velocity profiles are presented, where the FSAC-PP methods seemingly produces smoother profiles compared to the AC method, especially during the start-up of the simulation.

scholarly journals A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

2014 ◽  
Vol 16 (5) ◽  
pp. 1135-1180 ◽  
Author(s):  
László Könözsy ◽  
Dimitris Drikakis
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Flow Problems ◽  
Dual Time Stepping ◽  
Pressure Projection ◽  
The Stability

AbstractThis paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

Approximate Riemann solvers for the Godunov SPH (GSPH)

2014 ◽  
Vol 270 ◽  
pp. 432-458 ◽  
Author(s):  
Kunal Puri ◽  
Prabhu Ramachandran
Keyword(s):  
Riemann Solvers ◽  
Approximate Riemann Solvers

AUSM-Based High-Order Solution for Euler Equations

2012 ◽  
Vol 12 (4) ◽  
pp. 1096-1120 ◽  
Author(s):  
Angelo L. Scandaliato ◽  
Meng-Sing Liou
Keyword(s):  
Euler Equations ◽  
Splitting Method ◽  
High Order ◽  
Riemann Solvers ◽  
Carbuncle Phenomenon ◽  
Solution Accuracy ◽  
Matrix Vector ◽  
Approximate Riemann Solvers ◽  
Monotonicity Preserving ◽  
High Order Interpolation

AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables, even though they require additional matrix-vector operations. Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison. In addition, four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy. Finally, a measure for quantifying the efficiency of obtaining high order solutions is proposed; the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

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