Changes between Version 31 and Version 32 of u/erica/RoeSolver
 Timestamp:
 05/16/13 14:48:36 (11 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

u/erica/RoeSolver
v31 v32 34 34 }}} 35 35 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) RoePike 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 approachwe 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 constructs an averaged Jacobian directly, which must satisfy rigorous criteria such as hyperbolicity and conservation, and 2), the newer 'RoePike' 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. 37 37