A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coeffcients of an essentially non-oscillatory (MCENO) scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially non-oscillatory (ENO) scheme for its essential non-oscillation, total variation bounded (TVB), etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor (RT) instability with densities 1:3 and 1:100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the third-order ENO and fifth-order weighed ENO (WENO) schemes is 0.62:1:2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better effciency compared to the original ENO scheme.
The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research,because of its implications on the stability of stellar.By neglecting the viscosity and rotation of magnetic fluid,and assuming that the magnetic particles are irrotational and temperature insensitive,we obtain a simplified R-T instability model of magnetic fluid.For the interface tracing,we use five-order weighted essentially non-oscillatory(WENO) scheme to spatial direction and three-order TVD R-K method to time direction on the uniform mesh,respectively.If the direction of the external magnetic field is the same as that of gravity,the velocities of the interface will be increased.But if the direction of the external magnetic field is in opposition to the direction of gravity,the velocities of the interface will be decreased.When the direction of the external magnetic field is perpendicular to the direction of gravity,the symmetry of the interface will be destroyed.Because of the action which is produced by perpendicular external magnetic field,there are other bubbles at the boudaries which parallel the direction of gravity.When we increase the magnetic susceptibility of the magnetic fluids,the effects of external magnetic fields will be more distinct for the interface tracing.
