Kai Qu, Feiyu Zhang and Chanjie Li. Intelligent Control for Euler Equations based on Spline Method. Dynamic Systems and Applications 29 (2020) No. 7, 2445 – 2455

https://doi.org/10.46719/dsa20202976

ABSTRACT.
Inviscid multicomponent fluid plays an important role in fluid mechanics, the dynamics of inviscid multicomponent fluid can be modelled by the Euler equations. In this paper, a spline method which can preserve Euler equation was constructed. Spline method doesn’t need to construct grids which finite element method needs. To obtain a better solution on the boundary, bivariate spline proper subspace of  are primarily constructed. This subspace satisfies homogeneous boundary conditions on type-2 triangulations. A test was well solved and compared with the exact solutions, it indicates that spline method is reliable and has more accuracy.

Keywords:Bivariate spline; Finite element; Euler equations; Semi-discrete methods.