• Aerospace Engineering and Technology
• /
• v.8 no.1
• /
• pp.144-153
• /
• 2009

To study the plume effects in the rarefied region, the Direct Simulation Monte Carlo(DSMC) method is usually adopted because the plume field usually contains the entire range of flow regime from the near-continuum in the vicinity of nozzle exit through transitional state to free molecular at far field region from the nozzle. The objective of this study is to investigate the behaviors of a small monopropellant thruster plume in the rarefied region numerically using DSMC method. To deduce accurate results efficiently, the preconditioned scheme is introduced to calculate continuum flow fields inside thruster to predict nozzle exit properties used for inlet conditions of DSMC method. By combining these two methods, the rarefied flow characteristics of plume such as strong nonequilibrium near nozzle exit, large back flow region, etc, can be investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.37 no.9
• /
• pp.906-915
• /
• 2009

To study the plume effects in the vacuum area, the Direct Simulation Monte Carlo(DSMC) method is usually adopted because the plume field usually contains the entire range of flow regime from the near-continuum in the vicinity of nozzle exit through transitional state to free molecular at far field region from the nozzle. The objective of this study is to investigate the behaviors of a small monopropellant thruster plume in the vacuum area numerically using DSMC method. To deduce accurate results efficiently, the preconditioned scheme is introduced to calculate continuum flow fields inside thruster to predict nozzle exit properties used for inlet conditions of DSMC method. By combining these two methods, the vacuum flow characteristics of plume such as strong nonequilibrium near nozzle exit, large back flow area, etc, can be investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.32 no.3
• /
• pp.1-9
• /
• 2004

This study concentrates on the upwind schemes for convergence acceleration of the multigrid method for the Navier-Stokes equations. Comparative study of the upwind schemes in the Fourier space has been performed to identify why the second-order upwind scheme with enlarged stencil can be preconditioned better than the classical second-order upwind scheme. The full-coarsening multigrid method with implicit preconditioned multistage scheme has been implemented for verification of analysis. Numerical simulations on the inviscid and turbulent flows with the Spalart-Allmaras turbulent model have been performed. The results showed consistent trend with the analysis.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.30 no.4 s.247
• /
• pp.320-327
• /
• 2006

The computations of chemically reacting laminar and turbulent flows are performed using the preconditioned Navier-Stokes solver coupled with turbulent transport and multi-species equations. A low-Reynolds number $k-\varepsilon$ turbulence model proposed by Chien is used. The presence of the turbulent kinetic energy tenn in the momentum equation can materially affect the overall stability of the fluids-turbulence system. Because of this coupling effect, a fully coupled formulation is desirable and this approach is taken in the present study. Choi and Merkle's preconditioning technique is used to overcome the convergence difficulties occurred at low speed flows. The numerical scheme used for the present study is based on the implicit upwind ADI algorithm and is validated through the comparisons of computational and experimental results for laminar methane-air diffusion flame and $ H_2/O_2$ reacting turbulent shear flow. Preconditioning formulation shows better convergence characteristics than that of non-preconditioned system by approximately five times as much.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.8 s.179
• /
• pp.2100-2107
• /
• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.283-296
• /
• 2005

It is well known that the ordering of the unknowns can have a significant effect on the convergence of a preconditioned iterative method and on its implementation on a parallel computer. To do so, we introduce a block red-black coloring to increase the degree of parallelism in the application of the block ILU preconditioner for solving sparse matrices, arising from convection-diffusion equations discretized using the finite difference scheme (five-point operator). We study the preconditioned PGMRES iterative method for solving these linear systems.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.35 no.12
• /
• pp.1067-1074
• /
• 2007

A temperature preconditioning that modulates the derivative of density with respect to temperature is proposed to improve the convergence characteristics of the preconditioned Euler equations. Flows in a two-dimensional channel with a 10% circular bump in the middle of the channel were calculated at different speeds. The numerical dissipation terms of the Roe’s FDS scheme according to the temperature preconditioning are derived. It is shown that the temperature preconditioning accelerates convergence of the preconditioned Euler equations.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.627-645
• /
• 2007

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu\;:=-{\Delta}u+a(x,\;y)u_x+b(x,\;y)u_y+d(x,\;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu\;:=-{\Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.35-42
• /
• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.

• 한국전산유체공학회:학술대회논문집
• /
• 2005.10a
• /
• pp.169-177
• /
• 2005

A high resolution scheme for solving gas-liquid two-phase flows with cavitation is described. This scheme uses the curvilinear coordinate grid and solves the density based momentum equations for mixture of gas-liquid medium with a preconditioning method to treat both compressible and incompressible flow characteristics. The present preconditioned method is based on the Runge-Kutta explicit finite-difference scheme, and is improved by using the diagonalization, the flux difference splitting and the MUSCL-TVD schemes to save computational effort and to increase stability and resolvability, especially at gas-liquid contact surfaces. A homogeneous equilibrium cavitation model is used to treat the gas-liquid two-phase medium in cavitating flow as a locally homogeneous pseudo-single-phase medium. Therefore, it is easy to solve cavitating flow, including wave propagation, large density changes and incompressible flow characteristic at low Mach number. Some numerical results obtained by the present scheme are shown.