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.

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.

Effect of Slit Inclusions in Drag Reduction of Flow over Cylinders

2016 ◽  
Vol 846 ◽  
pp. 18-22
Author(s):  
Rohit Bhattacharya ◽  
Abouzar Moshfegh ◽  
Ahmad Jabbarzadeh
Keyword(s):  
Fluid Flow ◽  
Drag Reduction ◽  
Drag Coefficient ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Circular Cross Section ◽  
Finite Volume Methods ◽  
Turbulent Regime ◽  
Ansys Fluent ◽  
Comparison Of The Results

The flow over bluff bodies is separated compared to the flow over streamlined bodies. The investigation of the fluid flow over a cylinder with a streamwise slit has received little attention in the past, however there is some experimental evidence that show for turbulent regime it reduces the drag coefficient. This work helps in understanding the fluid flow over such cylinders in the laminar regime. As the width of the slit increases the drag coefficient keeps on reducing resulting in a narrower wake as compared to what is expected for flow over a cylinder. In this work we have used two different approaches in modelling a 2D flow for Re=10 to compare the results for CFD using finite volume method (ANSYS FLUENTTM) and Lattice Boltzmann methods. In all cases cylinders of circular cross section have been considered while slit width changing from 10% to 40% of the cylinder diameter. . It will be shown that drag coefficient decreases as the slit ratio increases. The effect of slit size on drag reduction is studied and discussed in detail in the paper. We have also made comparison of the results obtained from Lattice Boltzmann and finite volume methods.

A Low-Dissipation Second-Order Upwind Flux Formulation for Simulation of Complex Turbulent Flows

2015 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters ◽  
Edward A. Luke ◽  
Christopher I. Morris
Keyword(s):  
Turbulent Flows ◽  
Computational Cost ◽  
Weighted Average ◽  
Second Order ◽  
Least Square ◽  
Test Cases ◽  
Ansys Fluent ◽  
Cartesian Meshes ◽  
Low Dissipation ◽  
Linear Reconstruction

A numerical method is presented for low-dissipation, high-resolution finite-volume CFD simulations of turbulent flow. The convective fluxes in the governing equations are computed using a conventional upwind-biased second order scheme, with a modified linear reconstruction of face states from neighboring cells. The new scheme, dubbed optimization-based gradient reconstruction (OGRE), incorporates two key enhancements to improve performance. The first is an iterative least-square gradient computation procedure which minimizes the second-order dissipative error contribution to the face reconstruction on structured Cartesian meshes. The second is a slope limiting scheme which enforces local monotonicity near discontinuities without the detrimental effect of limiting in smooth regions of the flowfield. In addition, for density-based methods employing flux-difference splitting for the convective terms, a recently proposed weighted-average for obtaining the reconstructed face variable values is used, which improves accuracy in subsonic flow regions and eliminates the need for preconditioning. The new method has been implemented into the Ansys FLUENT and Loci-CHEM flow solvers, and is validated for several test cases by comparison to a conventional linear reconstruction implementation. Results clearly show the advantage of the new scheme over conventional upwind-biased second order schemes in terms of accuracy, particularly with regard to LES/DNS simulation. The most significant improvement is obtained for Cartesian meshes and low Mach number flows, but all test cases showed some level of improvement using the new scheme. The method is also quantified in terms of increased computational cost versus traditional methods. Based on results shown here, the method appears to represent a viable alternative to currently used centered and blended schemes in terms of accuracy, robustness, and computational expense.

Finite Volume Particle Method for Incompressible Flows

2014 ◽  
Vol 656 ◽  
pp. 72-80
Author(s):  
Sterian Danaila ◽  
Delia Teleaga ◽  
Luiza Zavalan
Keyword(s):  
Finite Volume ◽  
Meshless Method ◽  
Incompressible Flows ◽  
Particle Method ◽  
Finite Volume Methods ◽  
Particle Methods ◽  
Navier Stokes ◽  
Ansys Fluent ◽  
Manufactured Solutions ◽  
Method Of Manufactured Solutions

This paper presents an application of the Finite Volume Particle Method to incompressible flows. The two-dimensional incompressible Navier-Stokes solver is based on Chorin’s projection method with finite volume particle discretization. The Finite Volume Particle Method is a meshless method for fluid dynamics which unifies advantages of particle methods and finite volume methods in one scheme. The method of manufactured solutions is used to examine the global discretization error and finally a comparison between finite volume particle method simulations of an incompressible flow around a fixed circular cylinder and the numerical simulations with the CFD code ANSYS FLUENT 14.0 is presented.

scholarly journals Approximation of a Second-order Elliptic Equation with Discontinuous and Highly Oscillating Coefficients by Finite Volume Methods

2016 ◽  
Vol 8 (6) ◽  
pp. 34
Author(s):  
Bienvenu Ondami
Keyword(s):  
Finite Volume ◽  
Numerical Approximation ◽  
Elliptic Boundary ◽  
Finite Volume Methods ◽  
Second Order ◽  
Periodic Homogenization ◽  
One Dimensional ◽  
Elliptic Boundary Value ◽  
Oscillating Coefficients ◽  
Second Order Elliptic Equation

In this paper we consider the numerical approximation of a class of second order elliptic boundary value problems with discontinuous and highly periodically oscillating coefficients. We apply both classical and modified finite volume methods for the approximate solution of this problem. Error estimates depending on $\varepsilon$ the parameter involved in the periodic homogenization are established. Numerical simulations for one-dimensional problem confirm the theorical results and also show that the modified scheme has a smaller constant of convergence than the classical scheme based on harmonic averaging for this class of equations.

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