Flow simulation system based on high order space-time extension of flux reconstruction method

2015 ◽  
Author(s):  
Yi LU ◽  
Kai Liu ◽  
William N. Dawes
Keyword(s):  
Flow Simulation ◽  
Space Time ◽  
Simulation System ◽  
High Order ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Time Extension

A High-Order Flux Reconstruction Method for 2-D Vorticity Transport

2021 ◽  
Author(s):  
Adrin Gharakhani
Keyword(s):  
Finite Difference ◽  
Poisson Equation ◽  
Finite Difference Methods ◽  
Neumann Boundary ◽  
Normal Derivative ◽  
High Order ◽  
Benchmark Problems ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Vorticity Transport

Abstract A compact high-order finite difference method on unstructured meshes is developed for discretization of the unsteady vorticity transport equations (VTE) for 2-D incompressible flow. The algorithm is based on the Flux Reconstruction Method of Huynh [1, 2], extended to evaluate a Poisson equation for the streamfunction to enforce the kinematic relationship between the velocity and vorticity fields while satisfying the continuity equation. Unlike other finite difference methods for the VTE, where the wall vorticity is approximated by finite differencing the second wall-normal derivative of the streamfunction, the new method applies a Neumann boundary condition for the diffusion of vorticity such that it cancels the slip velocity resulting from the solution of the Poisson equation for the streamfunction. This yields a wall vorticity with order of accuracy consistent with that of the overall solution. In this paper, the high-order VTE solver is formulated and results presented to demonstrate the accuracy and convergence rate of the Poisson solution, as well as the VTE solver using benchmark problems of 2-D flow in lid-driven cavity and backward facing step channel at various Reynolds numbers.

Large Eddy Simulations for 3D Turbine Blades Using a High Order Flux Reconstruction Method

2013 ◽  
Author(s):  
Yi Lu ◽  
Kai Liu ◽  
W. N. Dawes
Keyword(s):  
Turbine Blade ◽  
High Order ◽  
Large Eddy Simulations ◽  
Complex Geometries ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Order Accuracy ◽  
Local Reconstruction ◽  
Low Pressure Turbine ◽  
Large Eddy

During the last decades, the improvements of both computational ability and numerical schemes have stimulated increasing industrial interest in the use of Large Eddy Simulations (LES) for practical engineering flow problems. However, almost all current approches cannot treat complex geometries at affordable cost to enable LES of industrial problems. A robust, parallel and efficient solver using a general unstructured grid & based on high order flux reconstruction formulation, which uses local reconstruction, is compact and written in differential form without a mass matrix, was developed and has proved the ability to get accurate LES results but using RANS scale meshes. This work is aimed at using flux reconstruction method to perform Large Eddy Simulations for complex geometries in more robust and highly efficient way. Both explicit Runge-Kutta method and implicit LU-SGS method are implemented with improvements as solvers for better performance on boundary layer meshes including large aspect ratio cells. The current solver is ported to GPU architectures and speed up ratios of different order accuracy are presented in this work. A local reconstruction method is introduced to generate high order curved boundary from readily available first order meshes. The large eddy simulations for low pressure turbine blade and low pressure turbine blade with endwall are presented in this work, resolved with total number of degree of freedoms up to 34 million to chieve fourth order accuracy using limited computational resource. The results show that this approach has the potential to obtain LES results of real-geometry problems with affordable computational costs.

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