Computational Fluid Dynamics 2004 pp 779-784
A One Point Shock Capturing Kinetic Scheme for Hyperbolic Conservation Laws
- Cite this paper as:
- Chandar D.D.J., Raghurama Rao S.V., Deshpande S.M. (2006) A One Point Shock Capturing Kinetic Scheme for Hyperbolic Conservation Laws. In: Groth C., Zingg D.W. (eds) Computational Fluid Dynamics 2004. Springer, Berlin, Heidelberg
5 Concluding Remarks
We have presented a new low dissipative kinetic scheme based on a modified Courant Splitting of the molecular velocity through a parameter φ. Conditions for the split fluxes derived based on equilibrium determine φ for a one point shock. It turns out that φ is a function of the Left and Right states to the shock and that these states should satisfy the Rankine-Hugoniot Jump condition. Hence φ is utilized in regions where the gradients are sufficiently high, and is switched to unity in smooth regions. Numerical results confirm a discrete shock structure with a single interior point when the shock is aligned with the grid.
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