计算力学学报
計算力學學報
계산역학학보
CHINESE JOURNAL OF COMPUTATIONAL MECHANICS
2015年
2期
239-242,268
,共5页
三维%复杂流动%Euler方程%RKDG方法%数值模拟
三維%複雜流動%Euler方程%RKDG方法%數值模擬
삼유%복잡류동%Euler방정%RKDG방법%수치모의
three dimensional%complex flows%Euler equations%RKDG method%numerical simulation
本文基于三维可压缩Euler方程，采用基于Runge‐Kutta时间离散的间断有限元方法（RKDG方法），对三维前台阶、三维Riemann问题和球Riemann等问题进行了模拟。结果表明，本文的RKDG方法能够在很少的网格内清晰地捕捉到三维复杂流场中的激波和接触间断；同时，将球Riemann问题中 z ＝0．4平面压强沿到对称轴距离的分布与文献中的近似精确解相比，吻合较好，这也验证了本文的RKDG方法不仅能够进行三维复杂流场的定性描述，也能够应用于三维复杂流场的定量计算。
本文基于三維可壓縮Euler方程，採用基于Runge‐Kutta時間離散的間斷有限元方法（RKDG方法），對三維前檯階、三維Riemann問題和毬Riemann等問題進行瞭模擬。結果錶明，本文的RKDG方法能夠在很少的網格內清晰地捕捉到三維複雜流場中的激波和接觸間斷；同時，將毬Riemann問題中 z ＝0．4平麵壓彊沿到對稱軸距離的分佈與文獻中的近似精確解相比，吻閤較好，這也驗證瞭本文的RKDG方法不僅能夠進行三維複雜流場的定性描述，也能夠應用于三維複雜流場的定量計算。
본문기우삼유가압축Euler방정，채용기우Runge‐Kutta시간리산적간단유한원방법（RKDG방법），대삼유전태계、삼유Riemann문제화구Riemann등문제진행료모의。결과표명，본문적RKDG방법능구재흔소적망격내청석지포착도삼유복잡류장중적격파화접촉간단；동시，장구Riemann문제중 z ＝0．4평면압강연도대칭축거리적분포여문헌중적근사정학해상비，문합교호，저야험증료본문적RKDG방법불부능구진행삼유복잡류장적정성묘술，야능구응용우삼유복잡류장적정량계산。
The 3rd order accurate Runge‐Kutta discontinuous Galerkin (RKDG ) method is developed to simulate three dimensional complex flow s ,such as three dimensional forw ard step problem ,three dimen‐sional Riemann problem and ball Riemann problem .Numerical results show that RKDG method can capture shocks and contact discontinuities in few grid points successfully .Furthermore ,the pressure distribution of z = 0 .4 plane in ball Riemann problem agrees well with the result in the reference by refined grids .This suggested that the RKDG method developed in this paper is not only able to qualita‐tively describe three‐dimensional complex flow s ,but also can be used in quantitative three‐dimensional complex flow field calculations .
