A local Lagrangian finite volume method for the numerical solution of conservation laws

An analytical cell averaging approach is applied to a local Lagrangian finite volume formulation of conservation laws describing the flow of a compressible fluid. After discretization, the approach eliminates the need for pointwise evaluation of fluxes and coupled with nonoscillatory interpolating functions, yields an accurate, conservative, stable scheme. This is done without the addition of any terms not derived from a direct discretization of terms in the original conservation law and without decoupling the system into characteristic fields. The development of the scheme is motivated and documented and its viability demonstrated by application to two one-dimensional fluid flow problems.