• Title/Summary/Keyword: High-Order WENO Scheme

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Development of a High-Order Accurate Hybrid Scheme Using the Central Flux and WENO Schemes (Central Flux Scheme과 WENO Scheme을 이용한 고차 정확도 Hybrid Scheme의 개발)

  • Kim D.;Kwon J. H.
    • 한국전산유체공학회:학술대회논문집
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    • 2005.04a
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    • pp.135-141
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    • 2005
  • A hybrid central-WENO scheme is proposed. The fifth order WENO-LF scheme is coupled with a central flux scheme at cell face. Two sub-schemes, the WENO-LF scheme and the central flux scheme, are switched by a weighting function. The efficiency and accuracy of the proposed hybrid central-WENO scheme is validated through several numerical experiments.

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HIGH-ORDER ADAPTIVE-GRID METHOD FOR THE ANALYSIS OF UNSTEADY COMPRESSIBLE FLOW (비정상 압축성 유동 해석을 위한 고차 정확도 적응 격자 기법의 연구)

  • Chang, S.M.;Morris, Philip J.
    • Journal of computational fluids engineering
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    • v.13 no.3
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    • pp.69-78
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    • 2008
  • The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

DEVELOPMENT OF A HIGH-ORDER NUMERICAL METHOD IN THE QUADRILATERAL ADAPTIVE GRIDS (사각형 적응 격자 고차 해상도 수치 기법의 개발)

  • Chang, S.M.;Morris, P.J.
    • 한국전산유체공학회:학술대회논문집
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    • 2006.10a
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    • pp.47-50
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    • 2006
  • In the aeroacoustic application of computational fluid dynamics, the physical phenomena like the crackle in the unsteady compressible jets should be based on very time-accurate numerical solution. The accuracy of the present numerical scheme is extended to the fifth order, using the WENO filter to the sixth-order central difference computation. However, the computational capacity is very restricted by the environment of computational power, so therefore the quadrilateral adaptive grids technique is introduced for this high-order accuracy scheme. The first problem is the multi-dimensional interpolation between fine and coarse grids. Some general benchmark problems are solved to show the effectiveness of this method.

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A New Code for Relativistic Hydrodynamics

  • Seo, Jeongbhin;Kang, Hyesung;Ryu, Dongsu
    • The Bulletin of The Korean Astronomical Society
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    • v.45 no.1
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    • pp.55.1-55.1
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    • 2020
  • In an attempt to investigate the nonlinear dynamics such as shock, shear, and turbulence associated with ultra-relativistic jets, we develop a new relativistic hydrodynamics (RHD) code based on the weighted essentially non-oscillatory (WENO) scheme. It is a 5th-order accurate, finite-difference scheme, which has been widely used for solving hyperbolic systems of conservation equations. The code is parallelized with MPI and OpenMP. Through an extensive set of tests, the accuracy and efficiency of different WENO reconstructions, and different time discretizations are assessed. Different implementations of the equation of state (EOS) for relativistic fluid are incorporated, As the fiducial setup for simulations of ultra-relativistic jets, we adopt the EOS in Ryu et al. (2006) to treat arbitrary adiabatic index of relativistic fluid, the WENO-Z reconstructions to minimize numerical dissipation without loss of stability, and the strong stability preserving Runge-Kutta (SSPRK) method to achieve stable time stepping with large CFL numbers. In addition, the code includes a high-order flux averaging along the transverse directions for multi-dimensional problems, and the modified eigenvalues for the acoustic modes to effectively control the carbuncle instability. We find that the new code performs satisfactorily simulations of ultra-relativistic jets.

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Assessment of Tip Shape Effect on Rotor Aerodynamic Performance in Hover

  • Hwang, Je Young;Kwon, Oh Joon
    • International Journal of Aeronautical and Space Sciences
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    • v.16 no.2
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    • pp.295-310
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    • 2015
  • In the present study, an unstructured mixed mesh flow solver was used to conduct a numerical prediction of the aerodynamic performance of the S-76 rotor in hover. For the present mixed mesh methodology, the near-body flow domain was modeled by using body-fitted prismatic/tetrahedral cells while Cartesian mesh cells were filled in the off-body region. A high-order accurate weighted essentially non-oscillatory (WENO) scheme was employed to better resolve the flow characteristics in the off-body flow region. An overset mesh technique was adopted to transfer the flow variables between the two different mesh regions, and computations were carried out for three different blade configurations including swept-taper, rectangular, and swept-taper-anhedral tip shapes. The results of the simulation were compared against experimental data, and the computations were also made to investigate the effect of the blade tip Mach number. The detailed flow characteristics were also examined, including the tip-vortex trajectory, vortex core size, and first-passing tip vortex position that depended on the tip shape.

Supersonic Base Flow by Using High Order Schemes

  • Shin, Edward Jae-Ryul;Won, Su-Hee;Cho, Doek-Rae;Choi, Jeong-Yeol
    • 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.

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MHD Turbulence in ISM and ICM

  • Cho, Hyunjin;Kang, Hyesung;Ryu, Dongsu
    • The Bulletin of The Korean Astronomical Society
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    • v.44 no.2
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    • pp.47.2-47.2
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    • 2019
  • Observations indicate that turbulence in molecular clouds of the interstellar medium (ISM) is highly supersonic (M >> 1) and strongly magnetized (β ≈ 0.1), while in the intracluster medium (ICM) it is subsonic (M <~1) and weakly magnetized (β ≈ 100). Here, M is the turbulent Mach number and β is the ratio of the gas to magnetic pressures. Although magnetohydrodynamic (MHD) turbulence in such environments has been previously studied through numerical simulations, some of its properties as well as its consequences are not yet fully described. In this talk, we report a study of MHD turbulence in molecular clouds and the ICM using a newly developed code based the high-order accurate, WENO (Weighted Essentially Non-Oscillatory) scheme. The simulation results using the WENO code are generally in agreement with those presented in the previous studies with, for instance, a TVD code (Porter et al. 2015 &, Park & Ryu 2019), but reveal more detailed structures on small scales. We here present and compare the properties of simulated turbulences with WENO and TVD codes, such as the spatial distribution of density, the density probability distribution functions, and the power spectra of kinetic and magnetic energies. We also describe the populations of MHD shocks and the energy dissipation at the shocks. Finally, we discuss the implications of this study on star formation processes in the ISM and shock dissipation in the ICM.

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MULTIDIMENSIONAL INTERPOLATIONS FOR THE HIGH ORDER SCHEMES IN ADAPTIVE GRIDS (적응 격자 고차 해상도 해법을 위한 다차원 내삽법)

  • Chang, S.M.;Morris, P.J.
    • 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).

PERFORMANCE OF LIMITERS IN MODAL DISCONTINUOUS GALERKIN METHODS FOR 1-D EULER EQUATIONS (1-D 오일러 방정식에 관한 Modal 불연속 갤러킨 기법에서의 Limiter 성능 비교)

  • Karchani, A.;Myong, R.S.
    • 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.