Comparative results for dam break problem in 1D shallow water equations: water height (left) and zoom on water height around the rarefaction and shock regions (right) at time t = 50s with 200 regular cells. For the FVC scheme, α = 0.7.
Embedded Files
Comparisons between numerical and experimental data of water depth h at Gauge 1 to 4 in the dam break in channels with 90 bend.
Mach number on the lower and upper wall M_max = 1.3891 (Fig on the left) and convergence history (Fig on the right).
The fields of concentration and flow velocity, along with contour level lines, illustrate the corresponding variation in water height in the Strait of Gibraltar, at t = 6 hours.
Giblatar_video2.mp4Circular_video.mp43DExplo_video.mp4Forward_video.mp4
The results generated by the FVC scheme for configurations 2 through 7. Pressure is represented by color, while 25 contours are used to represent density.
I have included here some codes written in MATLAB and Python for the linear transport equation, the Burgers' equation, the shallow water equation, and the Euler equations, along with the corresponding exact solutions. These scripts contain certain numerical schemes for comparison purposes. You will find the code directories in ZIP format attached. Please feel free to email me if you detect any errors or if you have any suggestions. Here are the codes.
1D shallow water equation and its exact solution
1D Euler equation and its exact solution
Manapy is an open-source library based on Python 3 that uses Numba and Pythran to accelerate functions and MPI to parallelize tasks. It provides all the necessary data structures to perform finite volume calculations on mixed 2D and 3D meshes, whether structured or unstructured. Manapy also offers an interface with several linear solvers, such as MUMPS and PETSc, to solve sparse matrix linear systems.
This work was conducted in collaboration with Mr. Imad Kissami (UM6P), an expert in parallel computing. It led to the development of the Manapy numerical library, dedicated to parallel finite volume methods on hybrid meshes. In this project, Mr. Kissami was responsible for the parallel implementation, while I focused on the mathematical formulation of the numerical schemes, their sequential implementation, and performance and convergence testing. The algorithms were successfully validated on realistic case studies, such as the modeling of the Strait of Gibraltar and compressible gas dynamics. This collaboration opens up promising perspectives for coupling with other physical models.
Page updated
Google Sites
Report abuse