• 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.

• Journal of computational fluids engineering
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• v.13 no.3
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• pp.35-43
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• 2008

A methodology for the simulation of compressible high Reynolds number flow over rigid and moving bodies on a structured Cartesian grid is described in this paper. The approach is based on a modified version of the Brinkman Penalization method. To avoid oscillations in the vicinity of the body and to simulate shcok-containing flows, a Weighted Essentially Non-Oscillatory scheme is used to discretize the spatial flux derivatives. For high Reynolds number viscous flow, two turbulence models of the two-equation Menter's SST URANS model and a two-equation Detached Eddy Simulation are implemented. Some simple flow examples are given to assess the accuracy of the technique. Finally, a moving grid capability is demonstrated.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.200-208
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• 2007

A methodology for the simulation of compressible high Reynolds number flow over rigid and moving bodies on a structured Cartesian grid is described in this paper. The approach is based on a modified version of the Brinkman Penalization method. To avoid oscillations in the vicinity of the body and to simulate shcok-containing flows, a Weighted Essentially Non-Oscillatory scheme is used to discretize the spatial flux derivatives. For high Reynolds number viscous flow, two turbulence models of the two-equation Menter's SST URANS model and a two-equation Detached Eddy Simulation are implemented. Some simple flow examples are given to assess the accuracy of the technique. Finally, a moving grid capability is demonstrated.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.39-47
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• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.116-121
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• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.207-231
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• 2023

This paper aims to improve the alternative formulation of the fifth- and sixth-order accurate weighted essentially non-oscillatory (AWENO) finite difference schemes. The first is to derive the AWENO scheme with sixth-order accuracy in the smooth region of the solution. Second, a new weighted polynomial functions combining the perturbed forms with conserved variable to the AWENO is constructed; the new form of tunable functions are invented to maintain non-oscillatory property. Detailed numerical experiments are presented to illustrate the behavior of the new perturbational AWENO schemes. The performance of the present scheme is evaluated in terms of accuracy and resolution of discontinuities using a variety of one and two-dimensional test cases. We show that the resulted perturbational AWENO schemes can achieve fifth- and sixth-order accuracy in smooth regions while reducing numerical dissipation significantly near singularities.

• Journal of the Korean Society of Propulsion Engineers
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• v.22 no.2
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• pp.66-73
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• 2018

A computational fluid dynamics simulation of pyrotechnic material combustion inside a cylindrical closed vessel was carried out using the Eulerian-Lagrangian method. The 5th order upwind WENO scheme and the improved delayed detached eddy turbulence model were implemented to capture shock waves. The flow structure was analyzed inside the cylindrical vessel with a pressure sensor installed at the side wall center. The analysis revealed that the pressure oscillated because of the shock wave vibration. Additionally, the simulation results with four different sensor tab depths implied that, inside the sensor tab, eddies were generated by the excessively large gap between the sensor diaphragm and the side wall. These eddies caused irregularity to the measured time-pressure curve, which is an undesirable characteristic.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.36.3-36.3
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• 2021

We study ultra-relativistic jets on several tens kpc scales through three-dimensional relativistic hydrodynamic (RHD) simulations using a new RHD code based on the weighted essentially non-oscillatory (WENO) scheme. Utilizing the high-resolution and high-accuracy capabilities of the new code, we especially explore the structures and energetics of nonlinear flows, such as shocks, turbulence, velocity shear in different parts of jets. We find that the mildly relativistic shocks which form in the jet backflow are most effective for the shock dissipation of the jet energy, while the turbulent dissipation is largest either in the backflow or in the shocked ICM, depending on the jet parameter. The velocity shear is strongest across the jet flow to the cocoon boundary. Our results should have important implications for the studies of high-energy cosmic-ray production in radio galaxies.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.426-432
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• 2004

Large-Eddy Simulation (LES) is applied for the simulation of compressible flat plate boundary with Reynolds number up to 5 X 10$^{5}$ . Numerical examples include shock/boundary layer interaction and boundary layer transition, aiming future application to the analysis of transonic fan/compressor cascades. The present LES code uses hybrid com-pact/WENO scheme for the spatial discretization and compact diagonalized implicit scheme for the time integration. The present code successfully predicted the bypass transition of subsonic boundary layer. As for supersonic turbulent boundary layer, mean and fluctuation velocity of the attached boundary, as well as the evolution of the friction coefficient and the displacement thickness both upstream and downstream of the separation region are all in good agreement with experiment. The separation point also agreed with the experiment. In the simulation of the shock/laminar boundary layer interaction, the dependence of the transition upon the shock strength is reproduced qualitatively, but the extent of the separation region is overpredicted. These numerical examples show that LES can predict the behavior of boundary layer including transition and shock interaction, which are hardly managed by the conventional Reynolds-averaged Navier-Stokes approach, although there needs to be more effort before achieving quantitative agreement.

• Journal of computational fluids engineering
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• v.21 no.2
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.