an:04141440
Zbl 0696.65078
Harten, Ami
ENO schemes with subcell resolution
EN
J. Comput. Phys. 83, No. 1, 148-184 (1989).
00171432
1989
j
65M06 35L65 76N15
essentially non-oscillatory finite difference scheme; equation of continuity; Euler equation; gas dynamics; numerical example
The author gives an idea for constructing an essentially non-oscillatory (ENO) finite difference scheme for problems containing the equation of continuity in the following form: \(u_ t+f(u)_ x=0,\quad u(0,x)=u_ 0(x).\) The construction is based on the observation that cell averages of a discontinuous piecewise-smooth function contain information about the location of the discontinuity within the cell.
The reader can find a detailed description of the main idea of ENO schemes and its generalization for second and higher order of accuracy. There is an application for Euler equation of gas dynamics. One can find a very interesting numerical example demonstrating the efficiency of proposed scheme.
Gy.Moln??rka