High Order Numerical Schemes for Linear Advection Equation on Hexagonal Mesh

Author: Natalia Nebulishvili
Annotation:

Bachelor’s thesis is about high order schemes for linear advection equation on hexagonal grid. There is constructed hexagonal mesh, Miura’s scheme and two new schemes are used for divergence calculation. For the first new scheme, a priori estimation is derived and convergence is proved. Barycentric numerical differentiation formula is used for the second scheme. Distinguish from Miura’s scheme directional derivatives are used for constructing both schemes. For integration in time the thesis includes several classical methods: Euler, Runge-Kutta and 4-th order SSP methods. The thesis also covers software implementation and test results as an appendix.

Lecture files:

პრეზენტაცია [ka]
მაღალი რიგის სქემები ექვსკუთხა ბადეზე წრფივი ადვექციის განტოლებისათვის [ka]