1-D advection in C++

See 1-D advection under API for the implementation of solving both linear and nonlinear 1-D advection method in C++.

Descriptions

_1DGrid

_1DGrid.H contains the class for creating a 1D Grid for advection to take place. It creates a grid on the physical domain [xmin, xmax] with finite resolution of grid points nx and ghost points ng.

solver

solver.H contains the 1D advection solver with linear methods like ftcs and upwinding methods, and nonlinear methods like predictor corrector and method of lines schemes. Some slope are also provides such as piecewise constant, centered, minmod, and MC.

Initial Condition

init_cond.H contains three example initial conditions, including tophat, sine, and gaussian.

Initial condition function should take the physical domain, e.g. x as input parameter.

Verification

To verify the validity of the advection solver, states shoudl return back to the original state after full cycles. Therefore, enter num_periods as a whole number, and see the evolved state comparing with the initial state. Initial state and final state should appear in the same directory for plotting purposes.

  • If num_periods is a whole number solver::solve() also prints out the relative error between the final and the initial state.

  • More accurate comparison is to plot the final and initial state. There is a pre-written python script that would plot all the dat files. Simply run the following command, where [dat files] are the dat files after running the advection solver. One could use *.dat to plot all the files.

    ./plot [dat files]

  • One can also do a runtime visualization of the data. In order to create runtime data after each time step, set runtime_dat = true for advection_solver. runtime data are stored inside folder runtime_data. See the visual by the following command:

There is a pre-wrritten unit_test.cpp that tests this mechanism and how to use the code. Simply run this file and plot all the output files. Or the following command

make unit_test DEBUG=TRUE
./unit_test
./plot *dat

There is also a pre-written runtime_test.cpp used for testing runtime visualization. To run the runtime_test.cpp for test, use the following command:

make runtime_test.cpp DEBUG=TRUE
./runtime_test
./plot runtime_data/* --animate