, 2011). The region of increased resolution in simulation M2M2-mid, for example, does not extend as far and does not demand as much refinement as in simulation M∞M∞-var, Fig. 3 and Fig. 5, but is sufficient to obtain comparable Froude numbers. The reduction in

the number of Veliparib mw vertices used in simulation M2M2-mid compared to simulation M∞M∞-var suggests that in the latter case more refinement has occurred than was necessary. Furthermore, with M2M2, the increase in resolution along the boundary is achieved without the need for spatial variation of the horizontal velocity weight, which, from the perspective of a model user, is clearly desirable. Again it is the ability of simulations with M2M2 to capture variations at a range

NVP-BEZ235 nmr of scales that facilitates the improved performance. The adaptive mesh simulations discussed above are guided by the metric, and the number of vertices in the mesh is essentially unconstrained (in practice a maximum number of vertices is set by the user, Section 3.3.4, and, here, the meshes produced with M∞M∞ and M2M2 do not reach this maximum, Fig. 6). Simulations that use different metrics (or even the same metric with different solution field weights) can have both a different average mesh resolution and a different distribution of mesh resolution. In order to separate the effects of these two factors, adaptive mesh simulations with a constrained number of mesh vertices are investigated. In these simulations, the number of mesh vertices is constrained by setting an upper and lower bound for the number of vertices to

2.0451×1042.0451×104, the same as the number of vertices in the coarsest fixed mesh, Table 2. The previously shown best performing M2M2 metric and, for comparison, the M∞M∞ metric are used with the solution field weights as in simulations M∞M∞-const, M2M2-coarse and M2M2-mid. The constrained simulations are denoted by an asterisk, M∞M∞-const∗, M2M2-coarse∗ and M2M2-mid∗, respectively. This set allows comparison between both different metrics and different solution field weights. Note, the constraint on the number of mesh vertices leads to a reduction in Protein Tyrosine Kinase inhibitor the number of vertices for M∞M∞-const∗ and M2M2-mid∗ compared to M∞M∞-const and M2M2-mid and an increase for M2M2-coarse∗ compared to M2M2-coarse, Fig. 6. The adapted mesh is subject to two constraints: the solution field weights and the bounds on the number of vertices. The adaptive mesh procedure adopted first computes the metric according to the solution field weights, as for the case with the unconstrained number of vertices. The metric is then scaled, if necessary, to coarsen or refine so that the number of vertices lies above or below the supplied lower or upper bound. This produces a mesh that attempts to meet the solution field weight criteria whilst satisfying the vertex constraint.