This test case solves the sole advection equation with explicit schemes.

Configurations

A cubic cavity of unit length is used to test advection schemes in the 3 directions.

Runtime parameters

Main parameters to run this test case are:

• advection schemes: "o1_upwind","o2_upwind","houc3","houc5","weno3","weno5","weno3_fd","weno5_fd"
• directions: [1,2,3]
• Courant number: [-0.1,0.1] the desired Courant number, signed in order to test backward advection.

Results

Pure sinus

Figure 1: Advection of a pure sinus with explicit schemes. Exact solution (in gray w/ crosses), first order upwind (o1_upwind, in red), second order upwind (o2_upwind, in orange), third order HOUC (houc3, in olive), third order WENO (weno3, in green w/ squares), third order WENO_FD (weno3_fd, in green w/ triangles), fifth order HOUC (houc5, in turquoise), fifth order WENO (weno5, in blue w/ squares), fifth order WENO_FD (weno5_fd, in blue w/ triangles),.

References