A high order accurate finite difference scheme is proposed for one-dimensional Euler equations. In the scheme a set of first three moments of each signal are preserved during the updating. The scheme is one of 5th order in space and 4th order in time. This feature is different from that in typical existing methods in which the use of the first three polynomials results in only 3rd order accuracy in space. The scheme has different features from the existing high order schemes, and the most noticeable are the simultaneous discretization both in space and time, and the use of moments of Riemann invariants instead of primitive physical variables. Numerical examples are given to show the accuracy of the scheme and its robustness for the flows involving shocks.
Bibliographical noteFunding Information:
The work presented here has been supported by the Department of Energy through Grants DE-FG02-87ER25035 and DE-FG02-94ER25207, and by the University of Minnesota through its Minnesota Supercomputer Institute when William Dai worked at the University of Minnesota.
- Finite difference
- Finite element
- Gas dynamics
- Hyperbolic system