Evolution Galerkin methods for hyperbolic systems in two space dimensions
Mathematics of Computation
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Stabilized residual distribution for shallow water simulations
Journal of Computational Physics
The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws
Journal of Computational Physics
Hi-index | 0.00 |
We present two new large time step methods within the framework of the well-balanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis forces, but results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We present two variants of large time step FVEG method: a semi-implicit time approximation and an explicit time approximation using several evolution steps along bicharacteristic cones.