Continuous and discontinuous Galerkin finite element methods of variational Boussinesq water-wave models

Koop, O.R. (2006) Continuous and discontinuous Galerkin finite element methods of variational Boussinesq water-wave models.

Abstract:There are many reasons to investigate the propagation of surface water waves in the sea. In this report Boussinesq models are studied, that can be applied for modeling free-surface waves propagating from the deep sea up into the surf zone. These models can become fairly complex and improving linear frequency dispersion properties of these Boussinesq models often invoke difficult higher-order terms in the resulting partial differential equations [18]. Among others, Broer [7, 8], Broer et al.[9]and Klopman et al.[19] propose, based on the variational principle for potential flows proposed by Luke [27], variational Boussinesq models to describe potential flows with dispersion. The advantage of these models is that energy is conserved and guaranteed to be positive, while mixed higher order spatial and temporal derivatives are avoided. The cost of this is that we additional unknown quantities, with associated elliptic partial differential equations, that are relatively simple to solve numerically [20]. In this report three variational models are considered, namely those of Luke [27], Klopman et al. [19] and Whitham [37], and they are extended including surface tension effects. Additionally, we integrated the motion of the fluid domain boundaries with our variational principles describing the fluid motion. We compare the linear dispersion relations of the three models and draw the conclusions that the Klopman variational Boussinesq model approximates the exact linear dispersion obtained from Luke variational principle for potential flow, better than the Whitham model.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:54 computer science
Programme:Computer Science MSc (60300)
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