CAJ | 학술논문

DG／FV 混合方法因其具有紧致、易于推广获得高阶格式及相比同阶精度 DG 方法计算量、存储量小等优点，自提出以来已成功应用于一维、二维标量方程和 Euler／N-S 方程的求解。综述了 DG／FV 混合方法的研究进展，重点介绍了 DG／FV 混合方法的空间重构算法、针对 RANS 方程的求解方法、隐式时间离散格式、数值色散耗散及稳定性分析、计算量理论分析，并给出了系列粘性流算例的计算结果，包括用于验证混合方法数值精度的库埃特流，以及方腔流、亚声速剪切层、低速平板湍流、NACA0012翼型湍流绕流等。数值计算结果表明 DG／FV 混合方法达到了设计的精度阶，且相比同阶 DG 方法计算量减少约40％，而隐式方法能大幅提高定常流的收敛历程，较显式 Runge-Kutta 的收敛速度提高1～2个量级。
DG／FV 혼합방법인기구유긴치、역우추엄획득고계격식급상비동계정도 DG 방법계산량、존저량소등우점，자제출이래이성공응용우일유、이유표량방정화 Euler／N-S 방정적구해。종술료 DG／FV 혼합방법적연구진전，중점개소료 DG／FV 혼합방법적공간중구산법、침대 RANS 방정적구해방법、은식시간리산격식、수치색산모산급은정성분석、계산량이론분석，병급출료계렬점성류산례적계산결과，포괄용우험증혼합방법수치정도적고애특류，이급방강류、아성속전절층、저속평판단류、NACA0012익형단류요류등。수치계산결과표명 DG／FV 혼합방법체도료설계적정도계，차상비동계 DG 방법계산량감소약40％，이은식방법능대폭제고정상류적수렴역정，교현식 Runge-Kutta 적수렴속도제고1～2개량급。
A concept of ‘static reconstruction’and ‘dynamic reconstruction’had been introduced for higher-order (third-order and higher)numerical methods in our previous work.Based on this concept,a class of DG/FV hybrid methods had been developed for the scalar equations and Euler/NS equations on trian-gular and Cartesian/triangular hybrid grids.In this paper,the recent progress of the DG/FV hybrid methods was presented.The basic idea of ‘hybrid reconstruction’,the procedure of solving NS equations with BR2 approach,and the implicit algorithm were reviewed briefly.And then the dissipative and dispersive proper-ty,as well as the stability,of the DG/FV hybrid schemes were analyzed.In order to show the high efficien-cy in the term of CPU time of the present DG/FV hybrid schemes,the computational costs were discussed and compared with the corresponding DG methods.The numerical accuracy was validated by some typical test cases of viscous flow,including the Couette flow,laminar flow in a square,compressible mixing layer problem,turbulent flows by RANS equations with S-A turbulent model over a flat plate and over NACA0012 airfoil.The accuracy study shows that the hybrid DG/FV method achieves the desired 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 (up to 40%)comparing with the traditional DG method with the same order of accuracy.Meanwhile,the implicit algorithm can accelerate the convergence history obviously, one to two orders faster than the explicit Runge-Kutta method.