CAJ | 학술논문

DG／FV 混合方法因其具有紧致性、易于推广至高阶及相比同阶 DGM 计算量、存储量小等优点，已成功应用于一维／二维标量方程和 Euler 方程的求解。在此基础上，将该方法推广于二维三角形／矩形混合网格上的 Navier-Stokes 方程数值模拟，将格式形式精度提高至4～5阶。物理量的空间重构及离散使用 DG／FV 混合重构方法；无粘通量计算采用 Roe 格式；粘性通量计算采用 BR2格式；时间方向离散采用高阶显式 R-K 方法或隐式方法。利用该方法计算了有解析解的 Couette 流动问题以验证几种格式的数值精度阶，并计算了层流平板流动和定常、非定常圆柱绕流问题等经典算例。计算结果表明 DG／FV 混合方法达到了设计的精度阶，在较粗的网格上亦能得到高精度的计算结果；定性分析和数值结果表明相比同阶 DG 方法单步计算量减少约40％。
DG／FV 혼합방법인기구유긴치성、역우추엄지고계급상비동계 DGM 계산량、존저량소등우점，이성공응용우일유／이유표량방정화 Euler 방정적구해。재차기출상，장해방법추엄우이유삼각형／구형혼합망격상적 Navier-Stokes 방정수치모의，장격식형식정도제고지4～5계。물리량적공간중구급리산사용 DG／FV 혼합중구방법；무점통량계산채용 Roe 격식；점성통량계산채용 BR2격식；시간방향리산채용고계현식 R-K 방법혹은식방법。이용해방법계산료유해석해적 Couette 류동문제이험증궤충격식적수치정도계，병계산료층류평판류동화정상、비정상원주요류문제등경전산례。계산결과표명 DG／FV 혼합방법체도료설계적정도계，재교조적망격상역능득도고정도적계산결과；정성분석화수치결과표명상비동계 DG 방법단보계산량감소약40％。
A concept of ‘static reconstruction’and ‘dynamic reconstruction’had been intro-duced for higher-order (third-order and higher)numerical methods in our previous work.Based on this concept,a class of hybrid DG/FV methods had been developed for the scalar equations and Euler equations on triangular and Cartesian/triangular hybrid grids.In this paper,the hybrid DG/FV methods are extended to 2D Navier-Stokes equations on triangular and Cartesian/triangu-lar hybrid grids.The BR2 scheme is employed to discretize the viscous terms.The numerical ac-curacy is validated by some typical test cases,including the Couette flow,laminar flows over a plate and a cylinder.The accuracy study shows that the hybrid DG/FV method achieves the de-sired order of accuracy,and they can capture the flow structure accurately.Qualitative analysis and numerical applications demonstrate that they can reduce the CPU time greatly than the tradi-tional DG method with the same order of accuracy.