An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid, part I: computational analysis
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Despite the numerical challenges, finite element method is used for the simulation of viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any process---are still missing. Either a very high computational cost is necessary or some limiting procedure is used by adding artificial dissipation to the system such that the accuracy is in danger. As a means of achieving a reliable and accurate method independent on the underlying process, we attack the problem by starting a discussion about the admissible governing equations leading to the necessary weak form without use of any stabilization or splitting schemes. We implement and solve the weak form by using open-source packages and present the accuracy by comparing the simulation to the closed-form solutions in the case of a linear viscous fluid. The computational method is accurate and robust for simulating isothermal and incompressible flows.
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