We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.

Lecture Notes in Computational Science and Engineering
European Conference on Numerical Mathematics and Advanced Applications
Scientific Computing

ten Thije Boonkkamp, J. H. M., Kumar, N., Koren, B., Van der Woude, D. A. M., & Linke, A. (2019). Nonlinear flux approximation scheme for Burgers equation derived from a local BVP. In Proceedings of ENUMATH (pp. 1015–1023). doi:10.1007/978-3-319-96415-7_96