Forward step

FORWARD STEP

Description of the problem

This problem was for the first time presented in the work of Woodward and P. Colella [1]. They solve the inviscid flow in the channel containing the forward step. The geometry of the problem can be viewed at Fig.1. There is the inlet part for x=0 and the outlet for x=3. Otherwise the impermeable walls are considered.

Fig.1: Forward step.

We prescribe the following initial conditions: density = 1.4, vector of velocty = (3.,0) and the pressure = 1. We are interested for the solution at time T=2.5.

Numerical results

Here we solve in fact the system of the Euler equations. The finite volume method was used for its discretizations. We present the results received by triangular and barycentric finite volume (see [2], [3]). Here are available our numerical results:

Triangular finite volumes

Barycentric finite volumes

Triangular finite volumes - color figures

Bibliography

[1] P. Woodward and P. Colella: The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks, J. of Comput. Phys, 54, pages 115-173, 1984

[2] J.Felcman and V.Dolejsi: Adaptive methods for the solution of the Euler equations in elements of the blade machines. ZAMM, 76:297-300, 1996.

[3] V.Dolejsi nad P. Angot: Finite volume methods on unstructured meshes for compressible flows. In F. Benkhaldoun and R. Vilsmeier eds., Finite Volumes for Complex Applications (Problems and Perspectives), pages 667--674, 1996.