High order well‐balanced scheme for river flow modeling

We propose a new numerical scheme based on the finite volumes to simulate the river flow in the presence of a variable bottom surface. Our approach is based on the Riemann solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave‐propagation form and can be extended to an arbitrary high order accuracy. The main goal is to construct the scheme, which is well‐balanced, i.e. maintains not only some special steady states, but all steady states which can occur.