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This is also clear from the normalized value of the wall (y+) which is desired to be one unit to avoid excessive refinement.
The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization.
The method allows for accurate treatment of the surface boundary conditions without the need for excessive refinement of the Cartesian mesh.
The mesh and timestep (ie, spatio-temporal discretisation) must be refined enough to capture the important haemodynamic behaviour of the modelled compartment (the final solution should be independent of mesh parameters), but without excessive refinement because this impacts negatively on computational resource and solution time (see online supplementary table S1).
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Sensitivity analysis indicates that reasonably accurate results can be achieved without excessive mesh refinement.
With this approach the user avoids excessive mesh refinement and does not need to obtain the stress at the critical distance in order to make the prediction.
Due to the multi-scale nature of flow regimes represented by the Brinkman equation, the standard Galerkin method requires excessive mesh refinement to achieve stable and accurate results.
We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient "black box" fast solver.
Wiggle-free numerical solutions can be obtained without invoking the upwind schemes or excessive mesh refinements.
As a consequence, we prevent numerical coalescence of the droplet and the liquid liquid interface without excessive (local) grid refinement.
Because simulation results using 3-level LGR and 4-level LGR are relatively close and further refinement may lead to excessive computational times, we regard the simulation result of 4-level LGR as the reference result to evaluate other simulations.
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