A Finite Element Scheme for Shock Capturing
Abstract
The representation of hydraulic jumps or shocks in compressible fluids is a difficult task for numerical models. These models require more smoothness than the analytic solution contains. For this reason these models are plagued with oscillations. The most widespread method is to smear the solution in the vicinity of the shock, giving up 0(1) errors, but restricting the error to the neighborhood of the jump or shock. This technique is called shock-capturing. In this report a method to capture hydraulic jumps formed by the shallow-water equations in a finite clement model is demonstrated. The model itself is two-dimensional. The method it relies upon is a Petrov-Galerkin approach in which the degree of upstream bias in the test function is based upon the characteristics of the convection matrix. Furthermore, in order to restrict the shock capturing to the vicinity of the jump, a method of jump detection is implemented which depends on the variation of mechanical energy within an element. The veracity of the model is tested by comparison of the predicted jump speed and magnitude with analytic and flume results. A comparison is also made to a flume case of steady-state supercritical lateral transition. Characteristics, Petrov-Galerkin, Supercritical, Finite element, Shallow-water equations, Two-dimensional, Hydraulic jump, Shock capturing.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1993
- Accession Number
- ADA270182
Entities
People
- R. C. Berger Jr.