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A High Resolution Low Dissipation hybrid scheme for Compressible Flows

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Chinese Journal of Aeronautics 2011年第4期24卷 417-424页

作者： YU Jian YAN Chao JIANG Zhenhua School of Aeronautic Science and Engineering Beihang University Beijing 100191 China

In this paper, an efficient hybrid shock capturing scheme is proposed to obtain accurate results both in the smooth region and around discontinuities for compressible flows. The hybrid algorithm is based on a fifth-order weighted essentially non-oscillatory （WENO） scheme in the finite volume form to solve the smooth part of the flow field, which is coupled with a characteristic-based monotone upstream-centered scheme for conservation laws （MUSCL） to capture discontinuities. The hybrid scheme is intended to combine high resolution of MUSCL scheme and low dissipation of WENO scheme. The two ingredients in this hybrid scheme are switched with an indicator. Three typical indicators are chosen and compared. MUSCL and WENO are both shock capturing schemes making the choice of the indicator parameter less crucial. Several test cases are carried out to investigate hybrid scheme with different indicators in terms of accuracy and efficiency. Numerical results demonstrate that the hybrid scheme in the present work performs well in a broad range of problems.

关键词： computational aerodynamics hybrid scheme characteristic variables weighted essentially non-oscillatory scheme high resolution low dissipation

Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme

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Journal of Hydrodynamics 2014年第2期26卷 187-198页

作者：房克照张哲邹志利刘忠波孙家文 State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology National Marine Environment Monitoring Center State Oceanic Administration

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen＇s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.

关键词： hybrid scheme Boussinesq equations TVD Riemann solver

A hybrid WENO scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

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Communications in Computational Physics 2023年第5期33卷 1270-1331页

作者： Yifei Wan Yinhua Xia School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026P.R.China

For steady Euler equations in complex boundary domains,high-order shockcapturing schemes usually suffer not only from the difficulty of steady-state convergence but also from the problem of dealing with physical boundaries on Cartesian grids to achieve uniform high-order *** this paper,we utilize a fifth-order finite difference hybrid WENO scheme to simulate steady Euler equations,and the same fifth-order WENO extrapolation methods are developed to handle the curved *** values of the ghost points outside the physical boundary can be obtained by applying WENO extrapolation near the boundary,involving normal derivatives acquired by the simplified inverse Lax-Wendroff *** equivalent expressions involving curvature and numerical differentiation are utilized to transform the tangential derivatives along the curved solid wall *** hybrid WENO scheme is robust for steady-state convergence and maintains high-order accuracy in the smooth region even with the solid wall boundary ***,the essentially non-oscillation property is *** numerical spectral analysis also shows that this hybrid WENO scheme has low dispersion and dissipation *** examples are presented to validate the high-order accuracy and robust performance of the hybrid scheme for steady Euler equations in curved domains with Cartesian grids.

关键词： Euler equations steady-state convergence curved boundary Cartesian grids WENO extrapolation hybrid scheme

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

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Water Science and Engineering 2015年第3期8卷 239-247页

作者： Jing Yin Jia-wen Sun Zi-feng Jiao National Marine Environment Monitoring Center State Oceanic Administration State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology

A total variation diminishing-weighted average flux （TVD-WAF）-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer （HLL） Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth- order monotone upstream-centered scheme for conservation laws （MUSCL）. The time marching scheme based on the third-order TVD Runge- Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.

关键词： hybrid scheme Finite volume method (FVM) Finite difference method (FDM) Total variation diminishing-weighted average flux (TVD-WAF) Boussinesq-type equations Nonlinear shallow water equations (NSWEs)

A hybrid FINITE ELEMENT scheme FOR INVISCID SUPERSONIC FLOWS

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Applied Mathematics and Mechanics(English Edition) 1997年第8期18卷 739-748页

作者：徐守栋吴望一 Department of Mechanics and Engineering Science Peking University Beijing P. R. China

A hybrid monotonous finite element algorithm is developed in the present paper, based on a second-order-accurate finite element scheme and a first-accurate monotonous one derived from the former by a unilateral lumping procedure in one dimensional case. The switch functions for the two dimensional Euler equation system are constructed locally, based on the gradient of the flow field, with special consideration on the information from neighboring elements. Examples show that the new scheme can eliminate oscillations near strong shocks obviously.

关键词： finite element hybrid scheme shocks

A hybrid EXPLICIT-IMPLICIT scheme FOR THE TIME-DEPENDENT WIGNER EQUATION

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Journal of Computational Mathematics 2021年第1期39卷 22-42页

作者： Haiyan Jiang Tiao Lu Xu Yin Department of Mathematics and Statistics Beijing Institute of TechnologyBeiing 100081China CAPT HEDPSLMAMIFSA Collaborative Innovation Center of MoESchool of Mathematical SciencesPeking UniversityBeijing 100871China Department of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value *** explicit-implicit time-splitting scheme is used for time integration and the second-order upwind finite difference scheme is used to dis-cretize the advection *** consistence error and the stability of the full discretization are analyzed.A Fourier spectral method is used to approximate the pseudo-differential operator term and the corresponding error is studied in *** final convergence result shows clearly how the regularity of the solution affects the convergence order of the pro-posed scheme.N umerical results are presented for confirming the sharpness of the *** scattering effects of a Gaussian wave packet tunneling through a Gaussian potential barrier are *** evolution of the density function shows that a larger portion of the wave is reflected when the height and the width of the barrier *** subject classification:65M06,65M70.

关键词： Finite diference method Spectral method hybrid scheme Error analysis Wigner equation.

An Adaptive High-Resolution and Low-Dissipation hybrid Energy Consistent/WENOCU scheme

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An Adaptive High-Resolution and Low-Dissipation Hybrid Energ...

A second-order finite difference scheme for singularly perturbed initial value problem on layer-adapted meshes

作者： Liang Li Hongbo Wang Dapeng Xiong Mingbo Sun Tao Tang Guoyan Zhao Xinxin Wang Science and Technology on Scramjet Lab National University of Defense Technology

We investigate the performance of the hybrid energy consistent/WENOCU4 scheme compared to the classical WENOCU4 *** is borne out that the hybrid scheme preserves excellent shock-capturing ability without numerical *** the meantime,the hybrid scheme can achieve more accurate representations of smooth flow features which indicates its low-dissipation ***,hybrid scheme significantly outperforms WENOCU4 for its superior computational ***,employing hybrid scheme is a much more cost-effective choice for the simulation of shock/turbulence interaction.

关键词： hybrid scheme Energy consistent WENOCU4 Low dissipation High resolution

来源： cnki会议评论

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第3期10卷 123-145页

作者： S.R.Sahu J.Mohapatra Department of Mathematics National Institute of Technology Rourkela India

In this paper,a second-order singularly perturbed initial value problem is considered.A hybrid scheme which is a combination of a cubic spline and a modified midpoint upwind scheme is proposed on various types of layer-adapted *** error bounds are established for the numerical solution and for the scaled numerical derivative in the discrete maximum *** is observed that the numerical solution and the scaled numerical derivative are of second-order convergence on the layer-adapted meshes irrespective of the perturbation *** show the performance of the proposed method,it is applied on few test examples which are in agreement with the theoretical ***,existing results are also compared to show the robustness of the proposed scheme.

关键词： Singular perturbation initial value problem hybrid scheme layer-adapted mesh uniform convergence

Analysis of Discontinuity Detectors and hybrid WCNS schemes Based on Waveform Recognition

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Communications in Computational Physics 2023年第7期34卷 418-455页

作者： Hao Zhang Yidao Dong Shichao Zheng Xiaogang Deng College of Aerospace Science and Engineering National University of Defense TechnologyChangsha410073China Institute of System Engineering Academy of Military SciencesBeijing 100082China

In this paper,we present a hybrid form of weighted compact nonlinear scheme(WCNS)for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones *** fulfill this algorithm,it is inseparable from the recognition ability of the discontinuity detector *** specific,a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities,while avoiding misjudgments of smooth *** classical detectors are classified into three basic types:derivative combination,smoothness indicators and characteristic ***,a new improved detector is proposed for *** they are analyzed through identifying a series of waveforms *** that,hybrid schemes using such indicators,as well as different detection variables,are examined with Euler equations,so as to investigate their ability to distinguish practical discontinuities on various *** results demonstrate that the proposed algorithm has similar performances to pure WCNS,while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler *** research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.

关键词： WCNS waveform detection troubled-cell indicator shock-capturing hybrid scheme