A Geometric Approach Towards Momentum Conservation
Using design tools based on finite difference and integral methods
D. Toshniwal (TU Delft - Mechanical Engineering)
Rene H.M. Huijsmans – Mentor (TU Delft - Ship Hydromechanics and Structures)
Marc Gerritsma – Mentor (TU Delft - Aerodynamics)
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Abstract
The equations governing fluid-flow are a set of partial differential equations, as is the case for a host of other continuous field problems. Analytical solutions to these problems are not always available and computers are unable to handle continuous representations of variables. This makes a finite-dimensional projection mandatory for all variables and this may result in a loss of information. At the same time, invoking the inherent association between physical field variables and geometric quantities, as seen in [1, 2, 3], it is known that stable discretisation schemes can be constructed. In this spirit, mimetic discretization strategies are based on minimizing the loss of information in going from a continuous to a discrete setting by making a clear distinction between exact/topological and approximate/constitutive relations in a physical law, and then focussing on an exact representation of the former and a suitable approximation of the latter. For further reading, please see [4, 5, 6, 7].