• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.156-157
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• 2003

A simple method is proposed to split the flux vector of the Euler equations by introducing two artificial wave speeds. The direction of wave propagation can be adjusted by these two wave speeds. This idea greatly simplifies the upwinding, and leads to a new family of upwind schemes. Numerical flux function for multi-dimensional Euler equations is formulated for any grid system, structured or unstructured. A remarkable simplicity of the scheme is that it successfully achieves one-sided approximation for all waves without recourse to any matrix operation. Moreover, its accuracy is comparable with the exact Riemann solver. For 1-D Euler equations, the scheme actually surpasses the exact solver in avoiding expansion shocks without any additional entropy fix. The scheme can exactly resolve stationary contact discontinuities, and it is also freed of the carbuncle problem in multi­dimensional computations.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.1
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• pp.10-17
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• 2008

In this paper an accurate and stable gridless method that can be applied to multi-dimensional convection problems is developed on a flow directional local grid. A two dimensional pure convection problem is calculated and more accurate and stable solution is obtained compared with other schemes in grid method. The tested numerical schemes include 1st-order upwind scheme, 2nd-order Leith scheme, 3rd-order MUSCL, and QUICK scheme. It is seen that more accurate results are expected when the schemes combined with a MMT control limiter.

• Journal of computational fluids engineering
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• v.8 no.4
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• pp.1-5
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• 2003

A Thin-layer Wavier-Stokes equations are applied for the hypersonic flow over blunt bodies with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and Van Leer are investigated to predict accurately the heating loads along the surface of the body. A mixed scheme has been presented for the differencing the convective terms and the mixed scheme is found to be less dissipative producing accurate solutions.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.56.2-56.2
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• 2011

Building a relativistic magnetohydrodynamic (RMHD) codes based on upwind schemes is a challenging project, because the characteristic wave structures for RMHDs has not yet been analytically given. We obtained an analytic expression of eigenvalues and eigenvectors of the flux Jacobian matrix of RMHDs for one-dimensional, isothermal flows with two velocity and magnetic field components (that is, x and y components only), which can be used to build numerical codes. The degeneracies were taken into account. Here, we present preliminary test results with an RMHD code based on the total variation diminishing (TVD) scheme.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1179-1194
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• 1992

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes(QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For pure convection oblique step flow test problem, QUICKUP, SMARTER and SHARPER schemes remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Cavity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.311-316
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• 2001

The thin-layer Navier-Stokes equations are solved for the hypersonic flow over blunt cone configurations with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and van Leer are investigated in their ability to accurately predict the heating loads along the surface of the body. A comparison with the second order extensions of these schemes is made and a hybrid scheme incorporating a combination of central differencing and flux-vector-splitting is presented. This scheme is also investigated in its ability to accurately predict heat transfer distributions.

• The KSFM Journal of Fluid Machinery
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• v.6 no.1 s.18
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• pp.23-29
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• 2003

Three-dimensional flow through a tubular centrifugal fan with airfoil type blades is analyzed, and the effects of turbulence model and numerical scheme on the results are investigated. Standard $k-{\epsilon}$ model and k - w model are tested as turbulence closures. The numerical schemes for convection terms, i.e., Upwind Differencing Scheme (UDS), Mass Weighted Skewed upstream differencing scheme (MWS), Linear Profile Skewed upstream differencing scheme (LPS), and Modified Linear Profile Skewed upstream differencing scheme (MLPS) are also tested, and the performances of these schemes coupled with two turbulence models are evaluated. The static pressure distributions are compared with experimental data obtained in this work, which shows that the $k-{\epsilon}$ model gives better results than the k-w model.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.91-97
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• 2001

The thin-layer Navier-Stokes equations are solved for the hypersonic flow over blunt cone configurations with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and van Leer are investigated in their ability to accurately predict the heating loads along the surface of the body. A comparison with the second order extensions of these schemes is made and a hybrid scheme incorporating a combination of central differencing and flux-vector-splitting is presented. This scheme is also investigated in its ability to accurately predict heat transfer distributions.

• 유체기계공업학회:학술대회논문집
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• 2001.11a
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• pp.23-29
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• 2001

Three-dimensional flow through a tubular centrifugal fan with airfoil type blades are analyzed using CFX-TASCflow. Standard k - $\epsilon$ model and k - $\omega$ model are used as turbulence closures. The numerical schemes for convetion terms, i.e., Upwind Differencing Scheme(UDS), Mass Weighted Skewed Upstream Differencing Scheme(MWS), Linear Profile Skewed Upstream Differencing Scheme(LPS), and Modified Linear Profile Skewed Upstream Differencing Scheme(MLPS) are also tested. And, the performance of these schemes coupled with two turbulence models are evaluated. Computational static pressure distributions are compared with experimental data obtained in this work.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.815-832
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• 1999

High-order weighted difference schemes with uniform meshes are considered for the convection-diffusion problem depending on Reynolds numbers. For small Reynolds numbers, a weighed cen-tral difference scheme is suggested since there is no boundary layer. For large Reynolds numbers, we propose a modified up wind method with an artificial diffusion in order to overcome nonphysical oscilla-tion of central schemes and obtain good accuracy in the boundary later. Existence and corresponding error estimates of the solution for the difference scheme have been shown. Numerical experiments are provided to back up the analysis.