A conservative degree adaptive HDG method for transient incompressible flows

Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work presents a series of numerical examples to show the inability of standard degree adaptive processes to accurate capture aerodynamic quantities of interest, in particular the drag. A new conservative projection is proposed and the results between a standard degree adaptive procedure and the adaptive process enhanced with this correction are compared. The examples involve two transient problems where flow vortices or a gust needs to be accurately propagated over long distances. \noindent \textbf{}Findings:polynomials with a lower degree. Due to the coupling of velocity-pressure in incompressible flows, the violation of the incompressibility constraint leads to inaccurate pressure fields in the wake that have a sizeable effect on the drag. The new conservative projection proposed is found to remove all the numerical artefacts shown by the standard adaptive process. Originality/value: This work proposes a new conservative projection for the degree adaptive process. The projection does not introduce a significant overhead because it requires to solve an element-by-element problem and only for those elements where the adaptive process lowers the degree of approximation. Numerical results show that with the proposed projection non-physical oscillations in the drag disappear and the results are in good agreement with reference solutions.