Verification of WENO-type extrapolation with different WENO schemes

Resumo

The usage of WENO-type extrapolation allows achieving high order and high resolution when solving
fluid dynamics numerical problems with the finite difference method and rectangular meshes. Developing new
modifications for this extrapolation implies better handling of boundary conditions. Hence, in this work, we are
interested in the verification of three WENO-type extrapolations together with four WENO schemes in smooth
and discontinuous test problems. Four different test problems modeled by the Euler equations will be solved with

the finite difference method, positivity-preserving Lax-Friedrichs flux, and strong stability preserving Runge-
Kutta. The first two are one-dimensional, and the others are two-dimensional. The one-dimensional discontinuous

problem is a severe test case for the WENO-type extrapolations. The two-dimensional discontinuous problem is
the double Mach reflection, which presents oblique shock and other nonlinear phenomena interacting with a wall.
We show that the design accuracy is being reached for smooth problems, that the discontinuities and nonlinear
phenomena are well captured, and we identify common features and areas of improvement for the WENO-type
extrapolations.