This test case solves the sole advection equation with implicit 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","o2_centered","quick","houc3"
• 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 implicit schemes. Exact solution (in gray w/ crosses), first order upwind (o1_upwind, in red), second order upwind (o2_upwind, in orange), second order centered (o2_centered, in pink), third order HOUC (houc3, in olive), third order QUICK (quick, in turquoise).

References