西安文理学院学报：自然科学版
西安文理學院學報：自然科學版
서안문이학원학보：자연과학판
Journal of Xi‘an University of Arts & Science:Natural Science Edition
2012年
1期
12-15
,共4页
FVWENO格式%TVD%Runge-Kutta时间离散方法%浸入边界Ghost%cell方法
FVWENO格式%TVD%Runge-Kutta時間離散方法%浸入邊界Ghost%cell方法
FVWENO격식%TVD%Runge-Kutta시간리산방법%침입변계Ghost%cell방법
FVWENO scheme%TVD Runge-Kutta time discrete method%immersed boundary Ghost cell method
首先构造二维FVWENO（finite volume weighted essentially non-oscillatory）格式：在二维空间模板上构造一个3次多项式.将此模板分割为8个较小的模板,每一个小模板上包含6个单元.在每一个小模板上构造一个2次多项式,要求多项式在单元上的平均值与需重构的物理量在同一单元上的平均值相等.之后,通过计算得到线性权,光滑指示器,非线性权.然后利用TVD Runge-Kutta时间离散方法得到时空一致高阶精度格式.最后,结合两种浸入边界Ghost cell方法,能针对复杂物体流动问题在结构网格上进行正确的数值模拟.
首先構造二維FVWENO（finite volume weighted essentially non-oscillatory）格式：在二維空間模闆上構造一箇3次多項式.將此模闆分割為8箇較小的模闆,每一箇小模闆上包含6箇單元.在每一箇小模闆上構造一箇2次多項式,要求多項式在單元上的平均值與需重構的物理量在同一單元上的平均值相等.之後,通過計算得到線性權,光滑指示器,非線性權.然後利用TVD Runge-Kutta時間離散方法得到時空一緻高階精度格式.最後,結閤兩種浸入邊界Ghost cell方法,能針對複雜物體流動問題在結構網格上進行正確的數值模擬.
수선구조이유FVWENO（finite volume weighted essentially non-oscillatory）격식：재이유공간모판상구조일개3차다항식.장차모판분할위8개교소적모판,매일개소모판상포함6개단원.재매일개소모판상구조일개2차다항식,요구다항식재단원상적평균치여수중구적물리량재동일단원상적평균치상등.지후,통과계산득도선성권,광활지시기,비선성권.연후이용TVD Runge-Kutta시간리산방법득도시공일치고계정도격식.최후,결합량충침입변계Ghost cell방법,능침대복잡물체류동문제재결구망격상진행정학적수치모의.
In this paper,the FVWENO（finite volume weighted essentially non-oscillatory） scheme is proposed on structured meshes.Firstly,we construct a 3-th degree polynomial on the big stencil.Then,we divide the associated stencil into eight smaller stencils which harbor six cells.And we construct different polynomials on different small stencils that match the cell averages of variables on all cells of the same small stencil.After that,we can get the linear weight,the smooth indicator and the nonlinear weight.Then,we use the TVD Runge-Kutta time discrete method to get fully discrete scheme both in space and time.Coupling with the two different immersed boundary Ghost cell methods,we can deal with the complex geometrical body simulations precisely.
