• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.2
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• pp.117-124
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• 2017

The performance of the colored Gauss-Seidel solver on CPU and GPU was investigated for the two- and three-dimensional heat conduction problems by using different mesh sizes. The heat conduction equation was discretized by the finite difference method and finite element method. The CPU yielded good performance for small problems but deteriorated when the total memory required for computing was larger than the cache memory for large problems. In contrast, the GPU performed better as the mesh size increased because of the latency hiding technique. Further, GPU computation by the colored Gauss-Siedel solver was approximately 7 times that by the single CPU. Furthermore, the colored Gauss-Seidel solver was found to be approximately twice that of the Jacobi solver when parallel computing was conducted on the GPU.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.93-98
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• 2001

An adaptive Cartesian grid method having the best elements of structured, unstructured, and Cartesian grids is developed to solve the steady two-dimensional Euler equations. The solver is based on a cell-centered finite-volume method with Roe's flux-difference splitting and implicit point Gauss-seidel time integration method. Calculations of several compressible flows are carried out to show the efficiency of the developed computer code. The results were generally in good agreements with existing data in the literature and the developed code has the good ability to capture important feature of the flows.

• Tribology and Lubricants
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• v.28 no.4
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• pp.160-166
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• 2012

This paper presents a Reynolds equation solver for hydrostatic gas bearings, implemented to run on graphics processing units (GPUs). The original analysis code for the central processing unit (CPU) was modified for the GPU by using the compute unified device architecture (CUDA). The red-black Gauss-Seidel (RBGS) algorithm was employed instead of the original Gauss-Seidel algorithm for the iterative pressure solver, because the latter has data dependency between neighboring nodes. The implemented GPU program was tested on the nVidia GTX580 system and compared to the original CPU program on the AMD Llano system. In the iterative pressure calculation, the implemented GPU program showed 20-100 times faster performance than the original CPU codes. Comparison of the wall-clock times including all of pre/post processing codes showed that the GPU codes still delivered 4-12 times faster performance than the CPU code for our target problem.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.10-18
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• 2016

Numerical boundary conditions are as important as the governing equations when analyzing the fluid flows numerically. An explicit boundary condition method updates the solutions at the boundaries with extrapolation from the interior of the computational domain, while the implicit boundary condition method in conjunction with an implicit time integration method solves the solutions of the entire computational domain including the boundaries simultaneously. The implicit boundary condition method, therefore, is more robust than the explicit boundary condition method. In this paper, steady compressible 2-Dimensional Navier-Stokes solver is developed. We present the implicit boundary condition method coupled with LU-SGS(Lower Upper Symmetric Gauss Seidel) method. Also, the explicit boundary condition method is implemented for comparison. The preconditioning Navier-Stokes equations are solved on unstructured meshes. The numerical computations for a number of flows show that the implicit boundary condition method can give accurate solutions.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.81-93
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• 2013

We consider a distributed optimal flux control problem: finding the potential of which gradient approximates the target vector field under an elliptic constraint. Introducing the Lagrange multiplier and a change of variables the Euler-Lagrange equation turns into a coupled equation of an elliptic equation and a reaction diffusion equation. The change of variables reduces iteration steps dramatically when the Gauss-Seidel iteration is considered as a solution method. For the elliptic equation solver we consider the Cell Boundary Element (CBE) method, which is the finite element type flux preserving methods.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.2
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• pp.44-53
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• 2007

A three-dimensional viscous flow solver has been developed for the prediction of the aerodynamic performance of hovering helicopter rotor blades using unstructured hybrid meshes. The flow solver utilized a vertex-centered finite-volume scheme that is based on the Roe's flux-difference splitting with an implicit Jacobi/Gauss-Seidel time integration. The eddy viscosity are estimated by the Spalart- Allmaras one-equation turbulence model. Calculations were performed at three operating conditions with varying tip Mach number and collective pitch setting for the Caradonna-Tung rotor in hover. Additional computations are made for the UH-60A rotor in hover. Reasonable agreements were obtained between the present results and the experiment in both blade loading and overall rotor performance. It was demonstrated that the present vertex-centered flow solver is an efficient and accurate tool for the assessment of rotor performance in hover.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.149-156
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• 2007

A three-dimensional inviscid flow solver has been developed based on unstructured meshes for the simulation of steady and unsteady flowfields around a generic fighter aircraft and for the investigation of the aerodynamic interference between the external stores and the tail surfaces. The flow solver is based on a vertex-centered finite-volume method and an implicit point Gauss-Seidel relaxation scheme. To validate the flow solver, calculations were made for a steady flow and the computed results were compared with experimental data. An unsteady time-accurate computation of the generic fighter aircraft with external stores at transonic flight conditions showed that the external stores cause undesirable vibration on the horizontal tail surface due to the mutual interference between their wake and the horizontal tail surface. It was shown that downward deflection of the trailing edge flap significantly reduces the undesirable interference effect.

• Journal of computational fluids engineering
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• v.5 no.2
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• pp.20-27
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• 2000

An unstructured implicit Euler solver is parallelized on a Cray T3E. Spatial discretization is accomplished by a cell-centered finite volume formulation using an upwind flux differencing. Time is advanced by the Gauss-Seidel implicit scheme. Domain decomposition is accomplished by using the k-way n-partitioning method developed by Karypis. In order to analyze the parallel performance of the solver, flows over a 2-D NACA 0012 airfoil and 3-D F-5 wing were investigated.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.193-200
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• 1999

An unstructured implicit Euler solver is parallelized on a Cray T3E. Spatial discretization is accomplished by a cell-centered finite volume formulation using an unpwind flux differencing. Time is advanced by the Gauss-Seidel implicit scheme. Domain decomposition is accomplished by using the k-way N-partitioning method developed by Karypis. In order to analyze the parallel performance of the solver, flows over a 2-D NACA 0012 airfoil and a 3-D F-5 wing were investigated.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.25-28
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• 2008

An aerodynamic calculation in hover of KUH main rotor blade is performed using a three-dimensional unstructured hybrid mesh viscous flow solver. The flow solver utilizes a vertex-centered finite-volume scheme that is based on the Roe's flux-difference splitting with an implicit Jacobi/Gauss-Seidel time integration. The eddy viscosity are estimated by the Spalart-Allmaras one-equation turbulence model. A solution-adaptive mesh refinement technique is used for efficient capturing of the tip vortex. Calculations are performed at several operating conditions with varying collective pitch setting for KUH main rotor blade in hover. Good agreements are obtained between the present and other results using HOST and CAMRAD II in overall rotor performance. It is demonstrated that the present vertex-centered flow solver is an efficient and accurate tool for the assessment of rotor performance in hover.