On a consistent high-order finite difference scheme with kinetic energy conservation for simulating turbulent reacting flows

Trisjono, P.,Kang, S.,Pitsch, H. Academic Press 2016 Journal of computational physics Vol.327 No.-

The main objective of this study is to present an accurate and consistent numerical framework for turbulent reacting flows based on a high-order finite difference (HOFD) scheme. It was shown previously by Desjardins et al. (2008) [4] that a centered finite difference scheme discretely conserving the kinetic energy and an upwind-biased scheme for the scalar transport can be combined into a useful scheme for turbulent reacting flows. With a high-order spatial accuracy, however, an inconsistency among discretization schemes for different conservation laws is identified, which can disturb a scalar field spuriously under non-uniform density distribution. Various theoretical and numerical analyses are performed on the sources of the unphysical error. From this, the derivative of the mass-conserving velocity and the local Peclet number are identified as the primary factors affecting the error. As a solution, an HOFD stencil for the mass conservation is reformulated into a flux-based form that can be used consistently with an upwind-biased scheme for the scalar transport. The effectiveness of the proposed formulation is verified using two-dimensional laminar flows such as a scalar transport problem and a laminar premixed flame, where unphysical oscillations in the scalar fields are removed. The applicability of the proposed scheme is demonstrated in an LES of a turbulent stratified premixed flame.

A comparison study on high-order bounded schemes:Flow of PTT-linear fluid in a lid-driven square cavity

Kerim Yapici 한국유변학회 2012 Korea-Australia rheology journal Vol.24 No.1

In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of 110-5 at all studied Weissenberg (We) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, i.e. primary vortex, are captured accurately up to We = 5 by all converged schemes.

A comparison study on high-order bounded schemes: Flow of PTT-linear fluid in a lid-driven square cavity

Yapici, Kerim 한국유변학회 2012 Korea-Australia rheology journal Vol.24 No.1

In this computational study, the convergence, stability and order of accuracy of several different numerical schemes are assessed and compared. All of the schemes considered were developed using a normalized variable diagram. Two test cases are considered: (1) two-dimensional steady incompressible laminar flow of a Newtonian fluid in a square lid-driven cavity; and (2) creeping flow of a PTT-linear fluid in a lid-driven square cavity. The governing equations are discretized to varying degrees of refinement using uniform grids, and solved by using the finite volume technique. The momentum interpolation method (MIM) is employed to evaluate the face velocity. Coupled mass and momentum conservation equations are solved through an iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. Among the higher-order and bounded schemes considered in the present study, only the CLAM, COPLA, CUBISTA, NOTABLE, SMART and WACEB schemes provide a steady converged solution to the prescribed tolerance of $1{ \times}10^{-5}$ at all studied Weissenberg ($We$) numbers, using a very fine mesh structure. It is found that the CLAM, COPLA, CUBISTA, SMART and WACEB schemes provide about the same order of accuracy that is slightly higher than that of the NOTABLE scheme at low and high Weissenberg numbers. Moreover, flow structures formed in the cavity, $i.e.$ primary vortex, are captured accurately up to $We$ = 5 by all converged schemes.

A Monotonic Limiter and Flux-Corrected Transport Approach for High-Order Time Integration Schemes

박상훈,이태영 한국기상학회 2013 Asia-Pacific Journal of Atmospheric Sciences Vol.49 No.5

A monotonic transport algorithm for a high-order time integration scheme is described in this paper. The algorithm is a modified version of an existing high-order time integration scheme,and is tested using a simple one-dimensional pulse and two-dimensional deformational flows. It is found that the new formulation can remove the error, caused by new maxima/minima and excessive smoothing, which occurs in scalar transport using the original extrapolation scheme. The results show that there may be potential for the high-order time integration scheme to be applied in numerical weather prediction models.

고해상도 수치기법을 이용한 피치 진동하는 날개주위의 비정상 아음속 유동해석

이경환 ( Kyeung Whan Lee ),김재수 ( Jae Soo Kim ),문지수 ( Ji Soo Moon ) 조선대학교 공학기술연구원 2015 공학기술논문지 Vol.8 No.1

Oscillating airfoil has been challenged for the dynamic stalls of airfoil and wind turbines at a high angle of attack. Especially, the pressure oscillation has a huge effect on noise generation, structure damage, aerodynamic performance and safety, because the flow has strong unsteadiness at a high angle of attack. In this paper, the unsteady aerodynamics coefficients were analyzed around a two dimensional oscillating NACA0012 airfoil at high angle of attack. The two dimensional unsteady compressible Navier-Stokes equation with a LES turbulent model was calculated by OHOC (Optimized High-Order Compact) scheme for space derivatives and 4th order Runge-Kutta scheme for time derivatives. The flow conditions are Mach number of 0.2 and Reynolds number of 2×10(4). The periodic angle of attack is given as . Several cases of the combinations of the mean and amplitude of angle of attacks have been calculated. The coefficients of lift and drag, pressure distribution, etc. are analyzed according to the pitching oscillation. Unsteady velocity field, periodic vortex shedding, the unsteady pressure distribution, and the acoustic fields are analyzed. The effects of these unsteady aerodynamic characteristics are analyzed by FFT at a high angle of attack.

Assessment of a High-Order High-Resolution ESWENO-P Scheme for AVI/BVI Problems

박상현,권오준,이상봉 한국항공우주학회 2022 International Journal of Aeronautical and Space Sc Vol.23 No.5

In the present study, two- and three-dimensional blade-vortex interaction problems were assessed by employing a Reynolds-averaged Navier–Stokes computational fluid dynamics solver based on mixed meshes. The meshes consisted of an unstructured near-body region and a Cartesian off-body region. To capture vortices with high resolution, WENO family schemes were used for computing inviscid fluxes on the Cartesian meshes. For the unstructured meshes, Roe’s flux difference splitting scheme was employed to compute inviscid fluxes. The resolution of the WENO family schemes was compared in terms of pressure coefficient distributions. It was found that, compared to the existing WENO family schemes, the ESWENO-P scheme is more stable and consistently resolves the airfoil/blade-vortex interaction problems with higher resolution.

로터 정지비행 해석을 위한 고차 정확도 비정렬 혼합격자계 기법 개발

황제영,정민규,권오준 한국항공우주학회 2014 한국항공우주학회 학술발표회 논문집 Vol.2014 No.4

본 연구에서는 복잡한 유동장과 형상 해석을 위한 비정렬 혼합격자계 기반의 삼차원 유동 해석자를 개발하였다. 물체 주변 영역에는 프리즘/사면체 격자를 사용하였고 물체를 포함하지 않는 영역에는 적응직교격자를 사용하였다. 수치적 소산을 줄이고 국부적인 유동특성을 포착하기 위해 고차정확도 기법(WENO)과 격자 적응기법(AMR)를 적용하였다. 서로 다른 두 격자계간의 유동 변수 내삽을 위해 중첩격자기법을 사용하였다. 개발된 유동 해석자의 검증을 위해 제자리 비행하는 S-76 로터 블레이드의 공력 특성을 예측하여 실험결과와 비교를 수행하였다. 고차 정확도 기법과 격자 적응을 수행한 격자에서 높은 해상도의 와류구조와 와류 짝 현상과 같은 유동특성이 더 잘 포착되었다. In the present study, a three-dimensional flow solver on unstructured mixed meshes was developed for flow simulations of complex geometry. Near-body region was made up of prismatic/tetrahedral meshes, while Off-body region was composed of adaptive Cartesian meshes. A high-order scheme and AMR were adopted to capture local flow characteristics with less numerical dissipation. An overset mesh technique was applied to transfer of flow variables between two different mesh blocks. To validate the accuracy of the current flow solver, the flow solver was applied to S-76 rotor blades in hover and the computed results were compared with experimental data. Ability to capture flow characteristics like vortex pairing were enhanced by adaptive mesh refinement and high-order accurate scheme.

High-order Compact Gas-kinetic Scheme for Flow Simulation

Fengxiang Zhao,Kun Xu 한국전산유체공학회 2022 한국전산유체공학회 학술대회논문집 Vol.2022 No.10

A fourth-order accurate finite difference scheme for the extended-Fisher-Kolmogorov equation

Tlili Kadri,Khaled Omrani 대한수학회 2018 대한수학회보 Vol.55 No.1

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}$-norm. Some numerical examples are given in order to validate the theoretical results.

A FOURTH-ORDER ACCURATE FINITE DIFFERENCE SCHEME FOR THE EXTENDED-FISHER-KOLMOGOROV EQUATION

Kadri, Tlili,Omrani, Khaled Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.