In this paper, we develop the high-order accurate essentially non-oscillatory (ENO) schemes on one and two-dimensional structured meshes in the finite volume formulation, and discuss their applications in hyperbolic conservation laws.
For hyperbolic conservation equation, the constant coefficients of firstorder upwind scheme for spacederivative are expanded to power series of gridspacings of both time and space, then the secondorder perturbational finite difference (PFD) scheme is obtained by determining the coefficients of the power series.
The properties of the solutions for the hyperbolic conservative Riemann problems:u_t+f_x=0,u=u_l(x<0),u=u_r(x>0). depend largely on the positions of u_r,u_l and the nucleation criterion.
The local existence of multiple shock fronts for hyperbolic conservation laws in higher dimensional space is established under the assumption that its frozen problem produces multiple uniformly stable planar shock fronts.
A system of nonlinear hyperbolic conservation equations, arising in the study of an evolution problem of a mixture of gases of interacting particles in the presence of only removal effects, is illustrated.