High-Order Spectral Volume Method for the Navier-Stokes Equations on Unstructured Grids

2004 ◽  
Author(s):  
Yuzhi Sun ◽  
Z.J. Wang
Keyword(s):  
Stokes Equations ◽  
Unstructured Grids ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Spectral Volume ◽  
Volume Method

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

scholarly journals GPU IMPLEMENTATION OF A VISCOUS FLOW SOLVER ON UNSTRUCTURED GRIDS

2016 ◽  
Vol 42 ◽  
pp. 1660167
Author(s):  
TIANHAO XU ◽  
LONG CHEN
Keyword(s):  
Graphics Processing Units ◽  
Stokes Equations ◽  
Unstructured Grids ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Competitive Advantages ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Volume Method ◽  
Graphics Processing

Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator

2012 ◽  
Vol 12 (1) ◽  
pp. 247-260 ◽  
Author(s):  
Ravi Kannan ◽  
Zhijian Wang
Keyword(s):  
Stokes Equations ◽  
High Order ◽  
High Order Accuracy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Riemann Solvers ◽  
Flow Problems ◽  
Spectral Volume ◽  
Original Scheme ◽  
New Formulation

AbstractThe concept of diffusion regulation (DR) was originally proposed by Jaisankar for traditional second order finite volume Euler solvers. This was used to decrease the inherent dissipation associated with using approximate Riemann solvers. In this paper, the above concept is extended to the high order spectral volume (SV) method. The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms. Numerical experiments were conducted to compare and contrast the original and the DR formulations. These experiments demonstrated (i) retention of high order accuracy for the new formulation, (ii) higher fidelity of the DR formulation, when compared to the original scheme for all orders and (iii) straightforward extension to Navier Stokes equations, since the DR does not interfere with the discretization of the viscous fluxes. In general, the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

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