During the later stages, the values of the background potential energy GSI-IX molecular weight perturbation tend towards those of the middle resolution fixed mesh, F-mid. The simulations that use M∞M∞ produce variable performance with respect to the mixing diagnostics. The simulation that uses M∞M∞ with a spatially varying solution field weight has comparable levels of diapycnal mixing to the fixed mesh simulation F-high1 during the propagation stage. During the oscillatory stage the simulations with M∞M∞ exhibit more diapycnal mixing than the higher resolution fixed meshes and continue to mix at all times. The simulations with MRMR do not offer an improvement over the simulations with M∞M∞ or M2M2 and use
at least 1.5–2 times as many vertices, Fig. 6. Comparison of adaptive mesh simulations with a constrained number of mesh vertices further demonstrate the improved performance with M2M2, Fig. 10 and Fig. 11. The weighting given to the smaller-scale fluctuations with M2M2 facilitates the formation of a more appropriate mesh, Fig. 5. This leads to improved representation of the Kelvin–Helmholtz billows
during the propagation stage and of the interface during the oscillatory stage and hence better representation of the diapycnal mixing. During the oscillatory stages, due to the diapycnal mixing, the curvature in the temperature field is not as large and the system also becomes less active. This leads to a coarsening of the mesh with M∞M∞, which tends to favour the strongest variations, and an increase in numerical diffusion, Fig. 3 and Fig. 8. A reduction in the solution field weights Ganetespib in vitro at later times would require additional user intervention but has the potential to improve performance of the simulations with M∞M∞ as
the system evolves. With MRMR, the mesh Nintedanib (BIBF 1120) is found to refine unnecessarily in regions of the domain where the velocity fields are near zero, Fig. 4. The temperature field, however, has near zero values at or near the interface, where resolution is required. The successful use of scaling by the local field value is, therefore, highly problem and field dependent. Using the global maximum or average of the magnitude of the field to scale the Hessian offers an alternative form of MRMR that has the potential to be utilised effectively in scenarios where an initially active flow diminishes over time. However, in the current form, the use of MRMR is not appropriate for the lock-exchange. The Froude numbers for the adaptive mesh simulations are also calculated. With the exception of simulation M∞M∞-const which uses M∞M∞ with spatially constant solution field weights, the values are found to be in good agreement with the higher resolution fixed meshes and hence published values Fig. 9 (Hiester et al., 2011). With simulations that use M2M2 and MRMR this is achieved with no need for user-defined spatial variation of the solution field weights.