A Comparison of Discretization Methods on Coarse Non-Uniform Grids

Dobelis, Elgars (2025) A Comparison of Discretization Methods on Coarse Non-Uniform Grids. Bachelor's Thesis, Applied Mathematics.

Preview	Text bAppM2025DobelisE.pdf Download (1MB) | Preview
	Text toestemming dobelis.pdf Restricted to Registered users only Download (203kB)

Abstract

This paper studies the behavior of discretization methods on coarse, non-uniform grids using the convection–diffusion equation as a test case. We implement grids with both abrupt and smooth transitions in grid cell size, and compare the performance of finite difference and finite volume methods. Our findings show that discretizations whose coefficient matrices preserve skew-symmetry when modeling convection yield more accurate results. Interestingly, this holds even if such schemes may exhibit larger local truncation error. In particular, we observe that only skew-symmetric discretization methods conserve energy when evolution of time is introduced, which aligns with underlying physical properties of convection. These results highlight the importance of selecting appropriate discretization methods when working with coarse, non-uniform grids and when aiming to preserve real-life properties.

Item Type:	Thesis (Bachelor's Thesis)
Supervisor name:	Veldman, A.E.P. and Verstappen, R.W.C.P. and Sterk, A.E.
Degree programme:	Applied Mathematics
Thesis type:	Bachelor's Thesis
Language:	English
Date Deposited:	10 Jul 2025 13:19
Last Modified:	10 Jul 2025 13:19
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/36082

Actions (login required)

View Item