| 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, and 2), the newer 'Roe-Pike' approach, 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, more widely used, approach that we will explore here. |
| | 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 (non-trivially) constructs an averaged Jacobian directly that must satisfy conditions such as hyperbolicity and conservation, and 2), the newer 'Roe-Pike' approach, 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, more widely used, approach that we will explore here. |
