• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.31 no.7
• /
• pp.1-8
• /
• 2003

Numerical characteristics of air chemistry associated with hypersonic flows are described and are compared with those of hydrogen oxygen combustion, applying the partially implicit time integration method to air chemistry. This paper reveals that the time integration of air chemistry needs a chemical Jacobian for stable calculations. However the positive real eigenvalues in air chemistry are relatively smaller than those of hydrogen combustion, and the numerical integration is less sensitive than that with combustion. lt is also found that the application of the partia1ly irnplicit method reduces the computing time without numerical instabilities.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.12
• /
• pp.1153-1161
• /
• 2010

An efficient solution method for harmonic balance techniques with Fourier transform is presented for periodic unsteady flow problems. The present partially-implicit harmonic balance treats the flux terms implicitly and the harmonic source term is solved explicitly. The convergence of the partially Implicit method is much faster than the explicit Runge-Kutta harmonic balance method. The method does not need to compute the additional flux Jacobian matrix from the implicit harmonic source term. Compared with fully implicit harmonic balance method, this partial approach turns out to have good convergence property. Oscillating flows over NACA0012 airfoil are considered to verify the method and to compare with results of explicit R-K(Runge-Kutta) and dual time stepping methods.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.36 no.4
• /
• pp.437-442
• /
• 2012

To analyze a multibody system, this paper proposes an implicit numerical integration method for joint coordinates subsystem synthesis method. To verify the proposed method, a multibody model for an unmanned robot vehicle, which consists of six identical independent suspension systems, is developed. The symbolic method is applied to compute the system Jacobian matrix for the implicit integration method. The proposed method is also verified by performing rough terrain run-over simulation in comparison with the conventional implicit integration method. In addition, to evaluate the efficiency of the proposed method, the CPU time obtained by using this method is compared with that obtained by using the conventional implicit method.

• Journal of Aerospace System Engineering
• /
• v.14 no.3
• /
• pp.17-23
• /
• 2020

In this paper, the efficient periodic unsteady flow analysis is developed by using a Chebyshev collocation operator applied to the time differential term of the governing equations. The partial implicit time integration method was also applied in the governing equation for a fluid, which means flux terms were implicitly processed for a time integration and the time derivative terms were applied explicitly in the form of the source term by applying the Chebyshev collocation operator. To verify this method, we applied the 1D unsteady Burgers equation and the 2D oscillating airfoil. The results were compared with the existing unsteady flow frequency analysis technique, the Harmonic Balance Method, and the experimental data. The Chebyshev collocation operator can manage time derivatives for periodic and non-periodic problems, so it can be applied to non-periodic problems later.

• Journal of computational fluids engineering
• /
• v.12 no.3
• /
• pp.29-40
• /
• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• Journal of computational fluids engineering
• /
• v.16 no.4
• /
• pp.72-83
• /
• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.04a
• /
• pp.30-40
• /
• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 1997.11a
• /
• pp.17-17
• /
• 1997

극초음속 여객기와 군사용 항공기에 대한 수요가 증가함에 따라서 새로운 개념의 다양한 추진기관이 연구가 진행되고 개발되어 왔다. 초음속 항공기의 속도 영역은 마하 10-20 정도가 되는데 이 속도 한계를 극복하기 위하여 초음속 연소 램제트 엔진(SCRamjet; Supersonic Combustion Ramjet)이 제안되었다. 스크램 제트를 개발하기 위해서는 연료와 산화제의 혼합 효율 문제, 화염의 안정화 문제, 벽면의 냉각에 관한 문제 등 몇 가지 기본적인 문제들을 해결해야 한다. Univ of Michigan에서 실험한 연소기를 모델로 본 연구에서는 연료와 공기의 혼합에 관한 수치 연구를 수행하였다. 다원 혼합기체에 관한 축대칭 Navier-Stokes 방정식을 지배 방정식을 이용하였고 비평형 화학반응식을 고려하였다. 공간 차분에는 유한 체적법을 이용하였다. 대류 플럭스 항은 Roe의 Upwind FDS 기법을 사용하여 차분하였고 점성항에는 중심 차분법을 이용하였다. 시간 적분법으로는 근사 자코비안과 LU분할 기법을 이용한 완전 내재적 방법이 쓰였다. 난류 모델로는 Mentor에 의해 제안된 2 방정식 k-$\varepsilon$/k-$\omega$ 혼합모델을 사용하였다. 유동장이 실험에서의 찍은 사진과 유사한 모습의 충격파 간섭을 수치 모사하였고 수소가 확산되는 모습과 함께 노즐 lip 주위의 재순환 영역에 대해서 살펴볼 수 있었다.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.11a
• /
• pp.42-47
• /
• 1999

In this study, we adopt the point symmetric Gauss-Seidel relaxation algorithm to obtain the steady state solution of the Navier-Stokes equations for the thermal and chemical nonequilibrium flow of air. All of the inviscid, viscous flux Jacobians and thermochemical source Jacobians are included in the implicit part Numerical simulation is performed for the thermal and chemical nonequilibrium flow over blunt body and computational results are presented. The convergence history and CPU time of the present computation are compared with the LU-SGS scheme which employs the approximate Jacobians.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2000.11a
• /
• pp.20-20
• /
• 2000

2개의 경사 충격파와 하나의 수직 충격파로 초음속 유동을 압축하는 초음속 공기 흡입구의 수치적 연구를 수행하였다. 지배방정식으로는 Navier-Stokes방정식을 사용하였고 난류모델로는 SST 모델을 사용하였다. 지배방정식의 점성항 계산에는 중심차분법을 사용하였고 대류항 계산에는 풍상차분법인 Roe의 FDS기법을 MUSCL기법과 결합하여 이용하였다. 유한 체적법을 이용하여 차분된 방정식은 LU분할 기법을 이용한 완전 내재적 방법으로 2차 정확도 시간 적분으로 비정상 과정의 연구를 수행하였다. 흡입구 배압을 정해주어야 하는 어려움을 해결하기 위해 흡입구 후면에 노즐을 달고 노즐의 면적을 조절하여 배압이 형성되도록 하였다.(중략)