• 유체기계공업학회:학술대회논문집
• /
• 2000.12a
• /
• pp.247-252
• /
• 2000

Flow through turbine flow meter is simulated by solving the incompressible Navier-Stockes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel Line relaxation method. The equations are solved steadily in rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. The standard k-$\epsilon$ model is employed to evaluate turbulent viscosity.

• Proceedings of the KSME Conference
• /
• 2000.11b
• /
• pp.573-578
• /
• 2000

Flow through turbine flow meter is simulated by solving the incompressible Navier-Stockes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved steadily in rotating reference frames and the centrifugal force and tile Coriolis force are added to the equation of motion. The standard $k-{\varepsilon}$ model is employed to evaluate turbulent viscosity. At first the stability and accuracy of the program is verified with the flow through a square duct with a $90^{\circ}$ bend and on the flat plate.

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

• 한국전산유체공학회:학술대회논문집
• /
• 1999.11a
• /
• pp.59-64
• /
• 1999

The Equations of Chemical kinetics ate very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the approximate chemical jacobian methods such as Gauss-Seidel, Jacobi partial jacobian and diagonalized jacobian that can be stable without full jacobian, We show that Gauss-Seidel jacobian method is stable and accurate as well as full jacobian and that this is more efficient in supersonic combustion problem about $20\%$ than the full jacobian method with same accuracy,

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

• Nuclear Engineering and Technology
• /
• v.55 no.7
• /
• pp.2516-2533
• /
• 2023

Several practical methods for accelerating the depletion calculation in a GPU-based Monte Carlo (MC) code PRAGMA are presented including the multilevel spectral collapse method and the vectorized Chebyshev rational approximation method (CRAM). Since the generation of microscopic reaction rates for each nuclide needed for the construction of the depletion matrix of the Bateman equation requires either enormous memory access or tremendous physical memory, both of which are quite burdensome on GPUs, a new method called multilevel spectral collapse is proposed which combines two types of spectra to generate microscopic reaction rates: an ultrafine spectrum for an entire fuel pin and coarser spectra for each depletion region. Errors in reaction rates introduced by this method are mitigated by a hybrid usage of direct online reaction rate tallies for several important fissile nuclides. The linear system to appear in the solution process adopting the CRAM is solved by the Gauss-Seidel method which can be easily vectorized on GPUs. With the accelerated depletion methods, only about 10% of MC calculation time is consumed for depletion, so an accurate full core cycle depletion calculation for a commercial power reactor (BEAVRS) can be done in 16 h with 24 consumer-grade GPUs.

• Tribology and Lubricants
• /
• v.28 no.4
• /
• pp.160-166
• /
• 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 the Korean Magnetics Society
• /
• v.6 no.1
• /
• pp.1-6
• /
• 1996

To simulate the characteristics of magnetic exchange coupling at the interface of MR/TbCo thin films, the directions of magnetizations were calculated by minimizing energy in the films. Newton method and Gauss-Seidel method were used. The width of M-H curve increased with TbCo anisotropy constant, and with the thickness of the transition region of TbCo layer. Hysteresis loop width became extremely narrow (less than 10 Oe of coercivity), when the TbCo transition region length was $400\;\AA$. Also the hysteresis loop of films with low interfacial exchange coupling constant was similiar to that of short transition region length. When interfacial exchange coupling constant was 1/100 of perfect coupling, hysteresis loop showed a coercivity of less than 10 Oe. Comparing the measured hysteresis loop of a fabricated sample with that of simulated one, exchange coupling con¬stant could be estimated.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.8
• /
• pp.1122-1133
• /
• 2003

Numerical characteristics of implicit upwind schemes, such as upwind ADI, line Gauss-Seidel (LGS) and point Gauss-Seidel (LU) algorithms, for Navier-Stokes equations have been investigated. Time-derivative preconditioning method was applied for efficient convergence at low Mach/Reynolds number regime as well as at large grid aspect ratios. All the algorithms were expressed in approximate factorization form and von Neumann stability analysis was performed to identify stability characteristics of the above algorithms in the presence of high grid aspect ratios. Stability analysis showed that for high aspect ratio computations, the ADI and LGS algorithms showed efficient damping effect up to moderate aspect ratio if we adopt viscous preconditioning based on min-CFL/max-VNN time-step definition. The LU algorithm, on the other hand, showed serious deterioration in stability characteristics as the grid aspect ratio increases. Computations for several practical applications also verified these results.

• The Journal of Engineering Research
• /
• v.3 no.1
• /
• pp.85-95
• /
• 1998

In this study, we consider a recursive procedure to obtain the stationary probability distribution for analyzing Coxian queueing networks with finite queues. This network deals with multiple class customers. Due to the state space representing multiple class customers, the sub-matrices corresponding to states can not be square matrices and can not be inverted. Therefore, we introduce more complex recursive method to avoid the singular problem. The open queueing network that we study consists of 3 parallel first-level sources linked to a single second level queue. We consider two types of schemes for entering a queue. The first scheme is assumed to be the first-blocked-first-enter (FBFE) and the second scheme is the higher-priority-first-enter (HPFE). Arrival and service times are assume to have a Coxian distribution with two phases. Comparison between the resulting using Gauss-Seidel method and recursive procedure will be shown.