Berkeley Fluids Seminar
University of California, Berkeley
Bring your lunch and enjoy learning about fluids!
March 31, 2014
Prof. Phillip Colella (Computer Science Division, Lawrence Berkeley National Laboratory)
High-Order Finite-Volume Methods for Computational Fluid Dynamics
Finite-volume methods are among the oldest and most successful discretization methods for computational fluid dynamics. Based on discretizing conservation laws in space by applying the divergence theorem over a collection of control volumes defined by a computational grid, they satisfy a discrete analogue of the local conservation properties of the underlying differential equations. This property is essential for simulation of shock waves, and helpful is simulating marginally-resolved problems in a variety of other settings. A principal disadvantage to these methods is that they have been typically second-order accurate in space. More sophisticated temporal discretizations for multi-physics problems and the numerical requirements for various representations of complex geometries have led to the need for higher-order methods. In this talk, we will describe one approach to designing high-order methods on locally-smooth, logically-rectangular grids, based on the use of higher-order quadrature rules for computing the average of fluxes over the boundaries of control volumes, combined with local refinement of grids. We will present examples of using this approach for simulating fluid dynamics on a sphere, kinetic models for plasmas, and classical problems in shock physics.