• 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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.723-728
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• 2008

We performed numerical analysis of base drag phenomenon, when a projectile with backward step flies into atmosphere at supersonic speed. We compared with other researchers. From our previous studies that were 2-dimensional simulation, we found out from sophisticated simulations that need dense mesh points to compare base pressure and velocity profile after from base with experimental data. Therefore, we focus on high order spatial disceretization over 3rd order with TVD such as MUSCL TVD 3rd, 5th, and WENO 5th order, and Limiters such as minmod, Triad. Moreover, we enforce to flux averaging schemes such as Roe, RoeM, HLLE, AUSMDV. In present, one dimensional result of Euler tests, there are Sod, Lax, Shu-Osher and interacting blast wave problems. AUSMDV as a flux averaging scheme with MUSCL TVD 5th order as spatial resolution is good agreement with exact solutions than other combinations. We are carrying out the same approaches into 3-dimensional base flow only candidate flux schemes that are Roe, AUSMDV. Additionally, turbulence models are used in 3-dimensional flow, one is Menter s SST DES model and another is Sparlat-Allmaras DES/DDES model in Navier-Stokes equations.

• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.1
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• pp.1-16
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• 2009

In this paper, we introduce two-phase versions of RoeM and AUSMPW+ schemes. Both schemes are originally developed for the gas dynamic problems, and have shown superior accuracy, efficiency and robustness. A new shock discontinuity sensing term is derived from the mixture equation of state, which is commonly used in the RoeM and AUSMPW+ schemes for the stable numerical flux calculation. The developed two-phase versions of the schemes are applied to several liquid-gas, large property discrepancy two-phase test problems, including several shock stability test problems. The results show that both schemes maintain the merits exhibited in gas dynamic problems even in two-phase flows.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.13-17
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• 2006

RoeM and AUSMPW+ schemes are two of the most accurate and efficient schemes which are recently developed for the analysis of single phase gas dynamics. In this paper, we developed two-phase versions of these schemes for the analysis of gas-liquid large density ratio two-phase flow. We adopt homogeneous equilibrium model (HEM) using mass fraction to describe different two phases. In the Eulerian-Eulerian framework, HEM assumes dynamic and thermal equilibrium of the two phases in the same computational mesh. From the mixture equation of state (EOS), we derived new shock-discontinuity sensing term (SDST), which is commonly used in RoeM and AUSMPW+ for the stable numerical flux calculation. The proposed two-phase versions of RoeM and AUSMPW+ schemes are applied on several air-water two-phase test problems. In spite of the large discrepancy of material properties such as density, enthalpy, and speed of sound, the numerical results show that both schemes provide very satisfactory solutions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.6
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• pp.569-574
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• 2020

Though the discontinuous Galerkin (DG) method has been developed and applied to shallow water equations mainly in explicit schemes, they have been criticized for the limitation in treatment of bottom friction terms and severe CFL conditions. In this study, an implicit scheme is devised and applied to some representative benchmark problems. The linear triangular elements were employed and the Roe numerical fluxes were adopted for convective fluxes. To preserve TVD property, the slope limiter was employed. As the case studies, the model is applied to the flow around the cylinders and the dam-break flow. Then, the results are compared with the experimental and numerical data of previous studies and good agreements were observed.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.43-52
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• 2007

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's, Godunov's, Osher's(physical order and natural order), Roe's, HLLE, AUSM, AUSM+, AUSMPW+ and M-AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.36-40
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• 2006

A comparative study on flux functions for the 2-dimensional Euler equations has been conducted. Explicit 4-stage Runge-Kutta method is used to integrate the equations. Flux functions used in the study are Steger-Warming's, van Leer's. Godunov's, Osher's(physical order and natural order), Roe's, HILE, AUSM, AUSM+ and AUSMPW+. The performance of MUSCL limiters and MLP limiters in conjunction with flux functions are compared extensively for steady and unsteady problems.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.78-84
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• 2011

CFD simulation has been conducted on a small scaled 4 nozzle clustered engine operating with air. In the present paper, the effects of grid size, turbulence models, flux difference methods have been compared. The results show that the base flows are somewhat different as the turbulence models, while Roe and AUSM flux differences produced almost the same results. Spalart-Allmaras turbulence model produces more accurate results rather than famous SST k-w model. The calculated Mach number and pressure profile in the engine base reveal the complex base flow structure, which is somewhat different from the generally estimated flow fields.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.5
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• pp.405-412
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• 2012

A flow control on airfoil installed a vortex cell for high efficiency wind turbine blade in stationary and dynamic stall conditions have been numerically investigated by solving the compressible Navier-Stokes equations. The numerical scheme is based on a node-based finite-volume method with Roe's flux-difference splitting and an implicit time-integration method coupled with dual time step sub-iteration. The computed result for the airfoil in the stationary showed that lift-drag ratio increases due to low pressure by the vortex cell. The oscillating airfoil with the vortex cell showed that the magnitude of hysteresis loop is reduced due to the enhanced vortex in the cell.