Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite Volume Flow Solvers

AIAA Journal ◽  
2016 ◽  
Vol 54 (10) ◽  
pp. 2961-2971 ◽  
Author(s):  
Johannes Löwe ◽  
Axel Probst ◽  
Tobias Knopp ◽  
Roland Kessler
Keyword(s):  
Finite Volume ◽  
Second Order ◽  
Volume Flow ◽  
Low Dissipation ◽  
Order Scheme ◽  
Low Dispersion

Scale-Resolving Simulations with a Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Flow Solvers

AIAA Journal ◽  
2016 ◽  
Vol 54 (10) ◽  
pp. 2972-2987 ◽  
Author(s):  
Axel Probst ◽  
Johannes Löwe ◽  
Silvia Reuß ◽  
Tobias Knopp ◽  
Roland Kessler
Keyword(s):  
Second Order ◽  
Low Dissipation ◽  
Order Scheme ◽  
Low Dispersion

A Non-Local Convective Flux Limiter for Upwind-Biased Finite Volume Simulations

2010 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Second Order ◽  
Numerical Dissipation ◽  
Ansys Fluent ◽  
First Order ◽  
Low Dissipation ◽  
Solution Convergence ◽  
Improve Accuracy ◽  
Non Local

Finite volume methods on structured and unstructured meshes often utilize second-order, upwind-biased linear reconstruction schemes to approximate the convective terms, in an attempt to improve accuracy over first-order methods. Limiters are employed to reduce the inherent variable over- and under-shoot of these schemes; however, they also can significantly increase the numerical dissipation of a solution. This paper presents a novel non-local, non-monotonic (NLNM) limiter developed by enforcing cell minima and maxima on dependent variable values projected to cell faces. The minimum and maximum values for a cell are determined primarily through the recursive reference to the minimum and maximum values of its upwind neighbors. The new limiter is implemented using the User Defined Function capability available in the commercial CFD solver Ansys FLUENT. Various simple test cases are presented which exhibit the NLNM limiter’s ability to eliminate non-physical oscillations while maintaining relatively low dissipation of the solution. Results from the new limiter are compared with those from other limited and unlimited second-order upwind (SOU) and first-order upwind (FOU) schemes. For the cases examined in the study, the NLNM limiter was found to improve accuracy without significantly increasing solution convergence rate.

A Low-Dissipation Optimization-Based Gradient Reconstruction (OGRE) Scheme for Finite Volume Simulations

2011 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters
Keyword(s):  
Objective Function ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Second Order ◽  
Ansys Fluent ◽  
Variable Field ◽  
Gradient Reconstruction ◽  
Low Dissipation ◽  
Upwind Discretization ◽  
Definition Of

Finite volume methods employing second-order gradient reconstruction schemes are often utilized to computationally solve the governing equations of transport. These reconstruction schemes, while not as dissipative as first-order schemes, frequently produce either dispersive or oscillatory solutions, especially in regions of discontinuities, and/or unsatisfactory levels of dissipation in smooth regions of the variable field. A novel gradient reconstruction scheme is presented in this work which shows significant improvement over traditional second-order schemes. This Optimization-based Gradient REconstruction (OGRE) scheme works to minimize an objective function based on the mismatch between local reconstructions at midpoints between cell stencil neighbors, i.e. the degree to which the projected values of a dependent variable and its gradients in a given cell differ from each of these values in neighbor cells. An adjustable weighting parameter is included in the definition of the objective function that allows the scheme to be tuned towards greater accuracy or greater stability. This scheme is implemented using the User Defined Function capability available in the commercially available CFD solver, Ansys FLUENT. Various test cases are presented that demonstrate the ability of the new method to calculate superior predictions of both a scalar transported variable and its gradients. These cases include calculation of a discontinuous variable field, several sinusoidal variable fields and a non-uniform velocity field. Results for each case are determined on both structured and unstructured meshes, and the scheme is compared with existing standard first- and second-order upwind discretization methods.

Low-dissipation low-dispersion explicit Taylor-Galerkin schemes from the Runge-Kutta kernels

2018 ◽  
Vol 17 (1-2) ◽  
pp. 88-113
Author(s):  
Mostafa Najafiyazdi ◽  
Luc Mongeau ◽  
Siva Nadarajah
Keyword(s):  
Time Integration ◽  
Second Order ◽  
Order Of Accuracy ◽  
Galerkin Scheme ◽  
Integration Schemes ◽  
Low Dissipation ◽  
Multi Stage ◽  
Time Integration Schemes ◽  
Runge Kutta ◽  
Low Dispersion

A multi-stage approach was adopted to investigate similarities and differences between the explicit Taylor-Galerkin and the explicit Runge-Kutta time integration schemes. It was found that the substitution of some, but not all, of second-order temporal derivatives in a Taylor-Galerkin scheme by additional stages makes it analogous to a Runge-Kutta scheme while preserving its original dissipative property for node-to-node oscillations. The substitution of all second-order temporal derivatives transforms Taylor-Galerkin schemes into Runge-Kutta schemes with zero attenuation at the grid cut-off. The application of this approach to an existing two-stage Taylor-Galerkin scheme yields a low-dissipation low-dispersion Taylor-Galerkin formulation. Two one-dimensional benchmarks were simulated to study the performance of this new scheme. The reverse process yields a general approach for transforming m-stage Runge-Kutta schemes into ( m−1)-stage Taylor-Galerkin schemes while preserving the same order of accuracy. The dissipation and dispersion properties for several new Taylor-Galerkin schemes were compared to those of their corresponding Runge-Kutta form.

scholarly journals Formation of Cavitation and Supercavitation in a Rectangular Shape Nozzle

2021 ◽  
Vol 10 (9) ◽  
Author(s):  
Espanta Ferdowsian
Keyword(s):  
Finite Volume ◽  
Continuity Equation ◽  
Momentum Equation ◽  
Second Order ◽  
Upwind Scheme ◽  
Finite Volume Scheme ◽  
Rectangular Shape ◽  
Cavitation Inception ◽  
Volume Scheme ◽  
Order Scheme

Flow inside a rectangular shape nozzle is simulated in this study. Finite volume scheme is utilized as the main solver for the current study. Second order scheme is utilized to discretize pressure. Second order upwind scheme is utilized for solving momentum equation. Then the momentum equation is coupled with the continuity equation to obtain the pressure and velocity at each cell. Cavitation inception and super cavitation is also found and discussed in this study and the results were also verified with previous Winklhofer et al. experiments.

scholarly journals Second-order discontinuous Galerkin flood model: Comparison with industry-standard finite volume models

2021 ◽  
Vol 594 ◽  
pp. 125924
Author(s):  
Janice Lynn Ayog ◽  
Georges Kesserwani ◽  
James Shaw ◽  
Mohammad Kazem Sharifian ◽  
Domenico Bau
Keyword(s):  
Discontinuous Galerkin ◽  
Finite Volume ◽  
Model Comparison ◽  
Second Order ◽  
Industry Standard ◽  
Flood Model ◽  
Volume Models
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