Title: An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid,
Abstract: Despite its numerical challenges, finite element method is used to compute
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 for a direct numerical solution (DNS) or some
limiting procedure is used by adding artificial dissipation to the system.
These stabilization methods are useful; however, they are often applied
relative to the element size such that a local monotonous convergence is
challenging to acquire. We need a computational strategy for solving viscous
fluid flow using solely the balance equations. In this work, we present a
general procedure solving fluid mechanics problems without use of any
stabilization or splitting schemes. Hence, its generalization to multiphysics
applications is straightforward. We discuss emerging numerical problems and
present the methodology rigorously. Implementation is achieved by using
open-source packages and the accuracy as well as the robustness is demonstrated
by comparing results to the closed-form solutions and also by solving
well-known benchmarking problems.