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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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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.
Sensitivity analysis indicates that reasonably accurate results can be achieved without excessive mesh refinement.
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.
This is also clear from the normalized value of the wall (y+) which is desired to be one unit to avoid excessive refinement.
As a consequence, we prevent numerical coalescence of the droplet and the liquid liquid interface without excessive (local) grid refinement.
"Without excessive political posturing, her film quietly dismantles stereotypes" (Scott).
It tackled this delicate subject without excessive moralism or melodrama.
Students these days "cannot imagine a system without excessive testing", it was argued.
Thorn sings without excessive affect, and has resonance throughout the range of her contralto voice.
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CEO of Professional Science Editing for Scientists @ prosciediting.com