Ravichandran, KS (1993) *Difference schemes for hyperbolic system of Conservation Laws 13; 13;.* In: CFD: Advances and Applications, 1993, Bangalore, India.

## Abstract

Conservation laws are a time dependent system of partial differential equations that define a set of relationships between the conserved variables (denoted by u) and the flux of these variables (denoted by f or F). It turns out that the conservation laws of mathematical physics are hyperbolic in the sense that the Jacobian matrix of the flux vector is diagonalizable with real eigenvalues and a complete set of eigenvectors. This mathematical property when interpreted physically means that signals propagate in the form of waves with finite speed and hence given initial data with compact support the solution for any finite t also has compact support. It is then conceptually apparent that given the data at any time t, it is in principle possible to compute the solution u(t + Delta t, x) and thus proceed indefinitely. The task of computing solutions therefore comes down to deriving suitable algorithms that do not break down during the computation and produce physically valid solutions of acceptable quality.

Item Type: | Conference or Workshop Item (Paper) |
---|---|

Uncontrolled Keywords: | Computational fluid dynamics;Conversation laws;Euler equations of motion;Finite difference theory;Hyperbolic differential equations;Partial differential equations; Eigenvalues;Eigenvectors;Navier-stokes equation;TVD schemes;Upwind schemes(mathematics) |

Subjects: | AERONAUTICS > Aerodynamics |

Division/Department: | Computational and Theoretical Fluid Dynamics Division |

Depositing User: | Mrs Manoranjitha M D |

Date Deposited: | 25 Jan 2007 |

Last Modified: | 24 May 2010 09:54 |

URI: | http://nal-ir.nal.res.in/id/eprint/3825 |

### Actions (login required)

View Item |