| | 36 | So the goal is to compute the wave speeds and associated eigenvalues and eigenvectors of the Jacobian matrix. There are 2 methods by which we can do this: 1) The Roe approach, which constructs an averaged Jacobian directly, which must satisfy rigorous criteria such as hyperbolicity and conservation, 2) Roe-Pike method, which avoids solving for the Jacobian and insteads develops algebraic expressions for the sought quantities based on averages of the initial data. It is the 2nd approach we will explore here. |
