Numerical Research Of Anisotropic Algorithm Based On CWENO Scheme And Its Application In Ferromagnetic Fluid

WENO(Weighted Essentially Non-oscillatory)scheme is an important high-precision scheme in Computational Fluid Dynamics.Later,people developed the CWENO(Central WENO)scheme based on the WENO scheme.The interpolation polynomial in the CWENO scheme uses the convex combination of the interpolation polynomial of the same template in order to achieve the highest possible accuracy in smooth areas and avoid false shocks.The CWENO scheme retains the advantages of the WENO scheme,which is better than the general central scheme.As a special fluid,ferromagnetic fluid has characteristics of noneconductivity and fluidity,which has been widely used in machinery,aerospace,magnetic,fluid power generation and other fields.Although there have been many advances in research on the modeling and numerical solution of ferrofluids,many problems including the RT instability problem of ferrofluid are still worth studying.In this paper,we simply describe the parabolic equation of ferrofluid and the CWENO scheme.Different accuracy and different types of anisotropic algorithms are proposed.Using different types of anisotropic algorithms,we focused on the calculation of RT instability under different magnetic field conditions.The numerical results verify that the anisotropic algorithm is effective for some problems,but it may destroy the symmetry of the numerical results when the grid size is large.Further numerical results show that different external magnetic fields will affect fluid flow instability to varying degrees.Using different types of anisotropic algorithms to calculate the RT instability problem in the absence of external magnetic fields and the presence of positive y-axis outward magnetic fields will not affect the symmetry of the numerical results.These results of this paper provide a certain reference for further research on the high-precision format that preserves symmetry.