Some Mandatory Benchmark Tests for Stability and Accuracy of High-Order Finite Difference Schemes
In Computational Fluid Dynamics (CFD) we have to deal with various types of phenomena with strong discontinuities at different length scales like turbulence or hypersonic flows. It is essential that the numerical techniques must provide accurate approximation to calculate the time and space-derivatives. This paper focuses on the behavior of the solution of some known numerical schemes in comparison with analytical solution provided here for the first time, applied on one-dimensional conservation law with different fluxes and non-usual different initial conditions. The results are very interesting in the sense that methods which report very good results on classical tests schemes were not able to accurately predict solutions that admit discontinuities and sharp gradients inside.
S. Dănăilă et al., "Some Mandatory Benchmark Tests for Stability and Accuracy of High-Order Finite Difference Schemes", Applied Mechanics and Materials, Vol. 859, pp. 52-56, 2017