Link to the source code for this example:

The console output of the program:

***************************************************************
* Running Example transient_ex3:
*   ./example-opt -i advection_2D.in
***************************************************************

Adding q1 variable using (CONSTANT, MONOMIAL) approximation to the system.
 EquationSystems
  n_systems()=1
   System #0, "Advection2D"
    Type "ClawSystem"
    Variables="q1"
    Finite Element Types="MONOMIAL", "JACOBI_20_00"
    Infinite Element Mapping="CARTESIAN"
    Approximation Orders="CONSTANT", "THIRD"
    n_dofs()=900
    n_local_dofs()=900
    max(n_local_dofs())=900
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=900
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 4.86667
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 5
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
      Number of Node Constraints = 0

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={2}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=3721
    n_local_nodes()=3721
  n_elem()=900
    n_local_elem()=900
    n_active_elem()=900
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true


==== ClawSystem ====
system name: Advection2D
LxF constant: 1.414
delta_t: 0.001
n_time_steps: 500
temporal_discretization_type: RK4
write_interval: 50


==== AdvectionSystem ====
u1 = 1, u2 = 1


plotting time step 50, time = 0.05

plotting time step 100, time = 0.1

plotting time step 150, time = 0.15

plotting time step 200, time = 0.2

plotting time step 250, time = 0.25

plotting time step 300, time = 0.3

plotting time step 350, time = 0.35

plotting time step 400, time = 0.4

plotting time step 450, time = 0.45

plotting time step 500, time = 0.5


***************************************************************
* Done Running Example transient_ex3:
*   ./example-opt -i advection_2D.in
***************************************************************