CAJ | 학술논문

将Caramana等人提出的相容算法思想和有限元方法相结合,提出三维笛卡儿坐标系中Lagrange流体力学的显式相容有限元方法.采用三线性六面体单元和交错网格进行空间离散,利用质量集中进行显式求解,无需求解线性代数方程组.时间离散可采用两步显式Runge-Kutta格式.用边人工粘性消除激波振荡,用子网格扰动压力抑制网格的非物理变形.给出若干标准算例.数值算例表明,该方法具有较高的计算精度和计算效率,同时具有很好的对称性和总能量守恒性,总能量计算误差为计算机浮点计算截断误差.
장Caramana등인제출적상용산법사상화유한원방법상결합,제출삼유적잡인좌표계중Lagrange류체역학적현식상용유한원방법.채용삼선성륙면체단원화교착망격진행공간리산,이용질량집중진행현식구해,무수구해선성대수방정조.시간리산가채용량보현식Runge-Kutta격식.용변인공점성소제격파진탕,용자망격우동압력억제망격적비물리변형.급출약간표준산례.수치산례표명,해방법구유교고적계산정도화계산효솔,동시구유흔호적대칭성화총능량수항성,총능량계산오차위계산궤부점계산절단오차.
We present an explicit compatible finite element method for fluid dynamics problems in three-dimensional Cartesian geometry. Trilinear brick elements with a staggered-grld placement of the spatial variables are used to discretize fluid equations. An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks. Subzonal perturbed pressure is adopted to resist spurious grid motions. Artificial viscosity forces and subzonal pressure forces agree well with general compatibility. Numerical examples show accuracy and robustness of the method.