DT
D. Toshniwal
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A Geometric Approach Towards Momentum Conservation
Using design tools based on finite difference and integral methods
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].
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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].