• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.99-104
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• 2001

This paper deals with the development of shock stable scheme that is free from shock instability. Roe's FDS is known to preserve good accuracy but to suffer from shock instability, i.e. the carbuncle phenomenon. As the first step toward the shock stable scheme, Roe's FDS is compared with HLLE scheme to identify the source of shock instability. Then control function f is introduced into the pressure term in Roe's FDS to cure shock instability. Various numerical tests concerned with shock instability are performed to demonstrate the shock stability of the proposed scheme.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.128-134
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• 2005

In the CFD area, the numerical analysis of high Mach number flow over a blunt-body poses many issues. Various numerical schemes have been developed to cover the issues, but the traditional schemes are still used widely due to the complexities of new schemes and intricacy of modifying the established codes. In the present study, the well-known Roe's FDS based on TVD-MUSCL scheme is used for the solution of very high Mach number three-dimensional flows posing carbuncle and non-physical phenomena in numerical analysis. A parametric study was carried out to account for the effects of the entropy fixing, grid configurations and initial condition. The carbuncle phenomena could be easily overcome by the entropy fixing, and the non-physical solution could be eliminated by the use of the modified initial condition regardless of entropy fixing and grid configurations.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.181-192
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• 2023

This work deals with the numerical modeling of dam-break flow over erodible bed. The mathematical model consists of the shallow water equations, the transport diffusion and the bed morphology change equations. The system is solved by central upwind scheme. The obtained results of the resolution of dam-beak problem is presented in order to show the performance of the numerical scheme. Also a comparison of central upwind and Roe schemes is presented.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.1
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• pp.11-19
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• 2010

A code is developed to simulate incompressible free surface flows using the Roe's flux-difference splitting scheme. An interface of two fluids is considered as a moving contact discontinuity. The continuities of pressure and normal velocity across the interface are enforced by the conservation law in the integral sense. The fluxes are computed using the Roe's flux-difference splitting scheme for two incompressible fluids. The interface can be identified based on the computed density distribution. However, no additional treatment is required along the interface during the whole computations. Complicated time evolution of the interface including topological change can be captured without any difficulties. The developed code is applied to simulate the Rayleigh-Taylor instability of two incompressible fluids in the density ratio of 7.2:1 and the broken dam problem of water-air. The present results are compared with other available results and good agreements are achieved for the both cases.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.1
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• pp.1-11
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• 2010

The definition of the speed of sound is reexamined since it is crucial in the numerical analysis of compressible real gas flows. The thermodynamic speed of sound (TSS), $a_{th}$, and the characteristic speed of sound (CSS), $a_{ch}$, are derived using generalized equation of state (EOS). It is found that the real gas EOS, for which pressure is not linearly dependent on density and temperature, results in slightly different TSS and CSS. in this formalism, Roe's approximate Riemann solver was derived again with corrections for real gases. The results show a little difference when the speeds of sound are applied to the Roe's scheme and Advection Upstream Splitting Method (AUSM) scheme, but a numerical instability is observed for a special case using AUSM scheme. It is considered reasonable to use of CSS for the mathematical consistency of the numerical schemes. The approach is applicable to multi-dimensional problems consistently.

• Journal of computational fluids engineering
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• v.6 no.4
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• pp.43-53
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• 2001

본 논문은 충격파 불안정성이 나타나지 않는 충격파 안정적인 수치기법의 개발을 목표로 하고 있다. Roe의 수치기법은 유동의 수치계산에 있어 높은 정확도를 보장하지만 carbuncle 현상과 같은 충격파 불안정성이 나타나는 것으로 알려져 있다. Roe의 수치기법과 HLLE 수치기법의 수치점성을 비교하여 충격파 불안정성의 원인을 살펴보았으며, Roe의 수치기법에 나타나는 반감쇠항에 마하수의 함수인 조절함수 f와 g를 도입하여 충격파 안정성을 획득하였다. 본 논문에서 제안된 수치기법을 다양한 유동문제에 적용하여 수치기법의 충격파 안정성과 정확성을 검증하였다

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.187-194
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• 2005

For the analysis of compressible multi-phase and real gas flows, characteristic form of Roe's Riemann solver was derived using real gas equation of state. It was extended to multi component reactive system considering variable specific heat. From this study, it is known that some correction should be made for the use of existing numerical algorithm. 1) Sonic speed and characteristic variable should be corrected with real gas effect. 2) Roe's average was applicable only with the assumption of constant properties. 3) Artificial damping term and characteristic variables should be corrected but their influences may not be significant.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.145-150
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• 2005

Generally, Compressible Navier-Stokes codes are used to solve high mach number flows. But, Most of high mach number flows embrace low mach number flows. This phenomenon results in low convergence rate and non-physical solution in CFD analysis. So Many researchers developed preconditioning technique to solve these problems. This Study presents how to modify previous compressible N-S computer code with little changes of structure into preconditioned compressible N-S code applying Roe's Approximate Riemann Solver. And this study show developed preconditioning code is very well operated at all mach number flows.

• Journal of the Korean Society of Propulsion Engineers
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• v.8 no.1
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• pp.27-37
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• 2004

The convergence characteristics of preconditioned Euler equations were studied. A perturbation analysis was conducted to understand the behavior of the preconditioned Euler equations. Various speed flows in a two-dimensional channel with a 10％ circular arc in the middle of the channel were calculated. Roe's FDS scheme was used for spatial discretization and the LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of pressure and velocity were maintained regardless of the Mach numbers but that the convergence characteristics of temperature were strongly related to the Mach number and became worse as the Mach number decreased. The perturbation analysis well explained the trend of the convergence characteristics and showed that the convergence characteristics are strongly related with the behavior o( the Preconditioning matrix.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.48-58
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• 1999

The Characteristic Flux Difference Splitting (CFDS) scheme designed to adapt the characteristic boundary conditions at the wall and inflow/outflow boundary planes satisfies Roe's property U, although the CFDS Jacobian matrix is decomposed by a product of elaborate transformation matrices and explicit eigenvalue matrix. When the CFDS algorithm, thus a variant of Roe's scheme, is applied straightforwardly to hypersonic flows over a blunt body, the strong bow shock gradually breaks down near the stagnation point. This numerical instability is widely observed by many researchers employing flux-difference method, known in the literature as the carbuncle phenomenon. Many remedies have been proposed and resulted in partial cures. When the idea of Sanders et al. which identifies the minimum eigenvalues near the discontinuity present is applied to CFDS method, it is shown that the instability problem can be controlled successfully. A few flux splitting methods have also been tested and results are compared against the Nakamori's Mach 8 blunt body flow.