We outline the implementation details of the non-conforming direct stiffness summation algorithm for the CG method and show that the mass conservation error is similar to the DG method.
The error in mass conservation is directly proportional to the residual in solving the discrete problem.
One original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation, to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid.
It is shown that if this is not handled properly, it can create large numerical errors (of up to 10%) and any oscillation in the flow field manifests itself in a similar error in the mass conservation.
A methodology preventing such errors for weighted essentially non-oscillatory (WENO) schemes is presented, in which modified WENO weights are used to solve the transport equation for mass fraction in conservative form to prevent temperature and species conservation errors.
However, the Taylor Hood element suffers from poor mass conservation which can lead to significant numerical mass balance errors for long-time simulations.
The SLOSH-VOF results are comparable to those from an Eulerian VOF method in terms of interface position errors, and improved with regard to mass conservation, even with CFL numbers increased up to one order of magnitude.
We prove mass conservation, unique solvability, energy stability, and the order of truncation error for the proposed methods.
In this work, analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme: (1) errors arising from the interpolations used to estimate the velocity on the cell faces, and (2) errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes.
Incorrect definition of reaction stoichiometries often results in stoichiometric inconsistencies - a common type of modelling error, defined as contradictions between the fundamental physical constraints of mass positivity and mass conservation [ 27].
