Collection of numerical codes presented in the Advanced Transport Phenomena (ATP) class at Politecnico di Milano.
The numerical codes are organized in the following folders:
-
lectures: codes presented and discussed in the ATP lectures -
practicals: codes and problems presented and discussed in the ATP practical sessions
The advection-diffusion-reaction equation is solved on a 1D domain using the finite-difference method. Constant, uniform velocity and diffusion coefficients are assumed. Spatial derivatives are discretized using 2nd-order, centered schemes. Time integration is carried out with different methods. Application to a metallic bar with fixed temperatures at the boundaries and possible heat exchange with the external environment.
- Time integration via ode45 solver: bar_1d_ode45.m
- Time integration via explicit (forward) Euler method: bar_1d_explicit_euler.m
- Time integration via implicit (backward) Euler method: bar_1d_implicit_euler.m
The advection-diffusion equation is solved on a 1D domain using the finite-difference method. Constant, uniform velocity and diffusion coefficients are assumed. The forward (or explicit) Euler method is adopted for the time discretization, while spatial derivatives are discretized using 2nd-order, centered schemes.
- Matlab script: advection_diffusion_1d.m
- Matlab live script: advection_diffusion_1d_live.mlx
The advection-diffusion-reaction equation is solved on a 1D domain using the finite-volume method. Constant, uniform velocity and diffusion coefficients are assumed. Spatial derivatives are discretized using 2nd-order, centered schemes. Time integration is carried out with ode15s solver. Application to a metallic bar with fixed temperatures at the boundaries and possible heat exchange with the external environment.
- Time integration via ode15s solver: bar_1d_ode15s.m
The advection-diffusion-reaction equation is solved on a 2D rectangular domain using the finite-difference method. Analyically prescribed velocity fields are assumed. Constant and uniform diffusion coefficients are assumed. Spatial derivatives are discretized using 2nd-order, centered schemes.
- Evaporating pool: evaporating_pool_2d_ode15s.m
- Tubular reactor: tubular_reactor_2d_ode15s.m
- Tubular reactor (multiple reactions): tubular_reactor_2d_multiple_reactions_ode15s.m
The advection-diffusion equation is solved on a 2D rectangular domain using the finite-difference method. Constant, uniform velocity components and diffusion coefficients are assumed. The forward (or explicit) Euler method is adopted for the time discretization, while spatial derivatives are discretized using 2nd-order, centered schemes.
- Matlab script: advection_diffusion_2d.m
- Matlab live script: advection_diffusion_2d_live.mlx
The Poisson equation is solved on a 2D rectangular domain using the finite-difference method. A constant source term is initially adopted. Spatial derivatives are discretized using 2nd-order, centered schemes. Different methods are adopted for solving the equation: the Jacobi method, the Gauss-Siedler method, and the Successive Over-Relaxation (SOR) method
- Matlab script: poisson_2d.m
- Matlab live script: poisson_2d_live.mlx
The same Poisson equation is solved by explicitly assembling the sparse matrix corresponding to the linear system arising after the spatial discretization
- Matlab script: poisson_2d_matrix.m
The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. See also: Lorenz system
- Matlab script: lorenz_equations.m
Numerical solution of a diffusion controlled growth 1D population balance equation using the Discrete Sectional Method (DSM) or the Quadrature Method of Moments (QMOM).
- Matlab script (DSM): dsm_diffusion_controlled_growth.m
- Matlab script (QMOM): qmom_diffusion_controlled_growth.m
- Matlab live script (DSM): dsm_diffusion_controlled_growth_live.mlx
- Matlab live script (QMOM): qmom_diffusion_controlled_growth_live.mlx