A finite-difference elasticity solver

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Research software practice, verification and validation · Research software practice, verification and validation

Scientific Computing for Physicists, Ch Are they the right equations? Solution verification, benchmarks and validation

Problem

A finite-difference elasticity solver, formally second order, reports the peak stress σ\sigma at a notch. Only two meshes are affordable: N=100N=100 gives σ2=249.400 MPa\sigma_2=249.400\ \mathrm{MPa} and N=200N=200 gives σ1=249.850 MPa\sigma_1=249.850\ \mathrm{MPa}, refinement ratio r=2r=2 (subscript 1 is the finer mesh). ((a)) Why can the observed order not be computed, and which safety factor applies? ((b)) Compute GCIfine\mathrm{GCI}_{\rm fine} (relative, dimensionless) using the formal order p=2p=2, and the absolute band it puts on σ1\sigma_1 in MPa. ((c)) Compute what GCIfine\mathrm{GCI}_{\rm fine} would be with Fs=1.25F_s = 1.25 had a third mesh confirmed p^=2\hat p = 2, and say why the two-mesh factor is larger.

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