Implementation of Explicit and Implicit Runge-Kutta methods to reduce the computational cost of pollutant transport modeling

Implementation of Explicit and Implicit Runge-Kutta methods to reduce the computational cost of pollutant transport modeling

Charis, I.

Civil Engineering and Geosciences

Geoscience & Engineering

Geo-Engineering

2016-11-21

Additional thesis report - Heimovaara et al. (2015) have developed a solute transport model (STM) so as to paint a dire portrait of the leachate generation and transport in the Braambergen landfill (located in the western portion of the Netherlands) with the ultimate goal of quantifying the chemical composition of the landfill's overall emissions. In fact, the model simulates the Chloride (Cl-) concentration in the outflowing from the landfill leachate and the mass of Cl- that remains in the landfill by using an ordinary differential equation (ODE) that describes dualporosity, mobile-immobile solute transport phenomena. This environmental model, developed in MATLAB, simulates these state variables by solving the aforementioned ODE by means of the well-known ode45 solver in MATLAB. In spite of that, the computational expense of the ode45 solver does not seem to be identical (~20-30 seconds of calculations). As is widely known, various ODE solvers usually require different computing times. Namely, the selection of the method for solving such insightful equations most often affects the time efficiency of ODE-based models. In the light of these considerations, this paper exploits the robustness of several explicit and implicit Runge-Kutta methods to solve the STM's ODE in an effort to make this model more cost-effective. By virtue of the results, the fourth order explicit Runge-Kutta method along with the fourth and sixth order implicit Runge-Kutta methods have successfully managed to drastically reduce the computational cost of the STM (~4-9 seconds of calculations).

Runge-Kutta
STM
ODE
Cl
ode45
Explicit
Implicit

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Student theses

student report

(c) 2016 Charis, I.