工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2014年
5期
719-727
,共9页
杨广辉%欧阳洁%刘帅强%杨斌鑫
楊廣輝%歐暘潔%劉帥彊%楊斌鑫
양엄휘%구양길%류수강%양빈흠
间断有限元%Level Set%非结构%界面%可压缩流
間斷有限元%Level Set%非結構%界麵%可壓縮流
간단유한원%Level Set%비결구%계면%가압축류
discontinuous Galerkin%level set%unstructured grids%interface%compressible flow
针对一般方法模拟具有运动界面的多介质可压缩流动问题计算量大、实施复杂的缺点,本文发展了一种基于非结构网格的数值模拟方法。该方法采用RKDG (Runge-Kutta Discontinuous Galerkin)方法的弱形式求解Euler方程,用强形式求解可压缩流场模拟中的Level Set方程,并用Simple Fix方法耦合两套方程的数值求解。二维多介质可压缩流的模拟表明:该方法成功地抑制了界面附近的非物理振荡,计算量小、实施简单,并可有效求解具有运动界面的多介质可压缩流动问题。
針對一般方法模擬具有運動界麵的多介質可壓縮流動問題計算量大、實施複雜的缺點,本文髮展瞭一種基于非結構網格的數值模擬方法。該方法採用RKDG (Runge-Kutta Discontinuous Galerkin)方法的弱形式求解Euler方程,用彊形式求解可壓縮流場模擬中的Level Set方程,併用Simple Fix方法耦閤兩套方程的數值求解。二維多介質可壓縮流的模擬錶明:該方法成功地抑製瞭界麵附近的非物理振盪,計算量小、實施簡單,併可有效求解具有運動界麵的多介質可壓縮流動問題。
침대일반방법모의구유운동계면적다개질가압축류동문제계산량대、실시복잡적결점,본문발전료일충기우비결구망격적수치모의방법。해방법채용RKDG (Runge-Kutta Discontinuous Galerkin)방법적약형식구해Euler방정,용강형식구해가압축류장모의중적Level Set방정,병용Simple Fix방법우합량투방정적수치구해。이유다개질가압축류적모의표명:해방법성공지억제료계면부근적비물리진탕,계산량소、실시간단,병가유효구해구유운동계면적다개질가압축류동문제。
Since the cost of general method is expensive and the implements is complicated to simulate the multimedia compressible flow with moving interface, we propose a RKDG (Runge-Kutta Discontinuous Galerkin) finite element method based on the unstructured grids in this paper. The weak form of RKDG method is used to solve the Euler equation, while the strong form of that is applied to solve the level set equation in the simulation of compressible flows. The numerical solutions of two equations are coupled by the Simple Fix method. The simulation of two-dimensional compressible multimedia flow shows that the numerical method can effectively restrain the non-physical oscillation. Moreover, the method has two advantages: one is low computing cost and the other is easy to implement, which make it is effective to simulate the compressible multimedia fluids with moving interfaces.