Mass Conservative Scheme Research Articles

Extrudate swell through an orifice die

The extrudate swell of a viscoelastic fluid through an orifice die is investigated by using a mixed finite element and a streamline integration method (FESIM), using a version of the K-BKZ model. The free surface calculation is based on a local mass conservation scheme and an approximate numerical treatment for the contact point movement of the free surface. The numerical results show a vortex growth and an increasing swelling ratio with the Weissenberg number. Convergence with mesh refinement is demonstrated, even at a high Weissenberg number of O(587), where the swelling ratio reaches a value of about 360%. In addition, it is found that the effective flow channel at the entrance region next to the orifice die is reduced due to the enhanced vortex growth, which may be a source of flow instability.

A Mass-Conserving Semi-Lagrangian Scheme for the Shallow-Water Equations

Abstract By generalizing the algorithm of Priestley for passively advected fields, a mass-conserving scheme for the coupled shallow-water equations is obtained. It is argued that the interpolation step of semi-Lagrangian schemes is the principal reason for their lack of formal conservation. The corrections introduced by the proposed algorithm to achieve conservation appropriately reflect the localized nature of the interpolation errors that induce its violation.

A two‐dimensional zonally averaged transport model including convective motions and a new strategy for the numerical solution

A two‐dimensional zonally averaged transport model of the atmosphere up to 10 mbar (∼33 km) has been developed. The transport is described by an effective stream function and a diffusion tensor derived from a three‐dimensional general circulation model. The numerical solution of the transport equations has been given special attention, and a positive definite mass conservative advection scheme which produces small numerical diffusion has been modified for use in the model. In addition to the vertical transport described by the transport equations, a parameterization of the vertical mixing due to convective clouds and frontal circulation is included in the model. The model has been tested with different tracers which indicated a realistic representation of the atmospheric transport.