Modified streamline upwind Petrov-Galerkin (SUPG) strategy for calculation of three-dimensional heterogeneous flow problems

作者：Su Bo^*; Han Xiangke

来源：Journal of Xi'an Jiaotong University, 2014, 48(3): 128-134.

DOI：10.7652/xjtuxb201403023

• Algebraic equations
• Calculation results
• Different densities
• Finite element schemes
• Governing equations
• Interpolating functions
• Petrov-Galerkin
• Splitting algorithms

By introducing the dual-time stepping method and the variable splitting algorithm, a modified SUPG strategy is developed based on the stable streamline upwind Petrov-Galerkin (SUPG) finite element method, where the traditional assumption of constant density for incompressible flow problem is abandoned and the density transportation equation is introduced into the governing equations. The velocity and pressure fields are discretized with interpolating function of the same order, thus finite element scheme of the modified SUPG strategy gets simple and clear, and the order of algebraic equations is reduced. The dual-time stepping method is also introduced to enhance calculation stability of the SUPG strategy for complex unsteady problems. A free flow with heterogeneous, unsteady field of three-dimensional rectangular pipe under gravity and the whole relative motion between two types of liquids with different density are analyzed. The calculation results indicate that the velocity and pressure fields distribute and transmit smoothly with time and no numerical wave occurs in the case of greater time steps; the vortex position and its varying regulation coincide well with the results in the classic literatures without jumps and discontinuities. Example proves the numerical stability and accuracy of the modified SUPG method.

• 出版日期2014