Pressure‐stabilized maximum‐entropy methods for incompressible Stokes

Abstract

SUMMARYWe present a parameter-free stable maximum-entropy method for incompressible Stokes flow. Derived from a least-biased optimization inspired by information theory, the meshfree maximum-entropy method appears as an interesting alternative to classical approximation schemes like the finite element method. Especially compared with other meshfree methods, e.g. the moving least-squares method, it allows for a straightforward imposition of boundary conditions. However, no Eulerian approach has yet been presented for real incompressible flow, encountering the convective and pressure instabilities. In this paper, we exclusively address the pressure instabilities caused by the mixed velocity-pressure formulation of incompressible Stokes flow. In a preparatory discussion, existing stable and stabilized methods are investigated and evaluated. This is used to develop different approaches towards a stable maximum-entropy formulation. We show results for two analytical tests, including a presentation of the convergence behavior. As a typical benchmark problem, results are also shown for the leaky lid-driven cavity. The already presented information-flux method for convection-dominated problems in mind, we see this as the last step towards a maximum-entropy method capable of simulating full incompressible flow problems.

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