A finite-difference wave-equation 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 wave-equation solver, formally second order, estimates the phase speed

c

of a travelling pulse on three grids with refinement ratio

r=2

N=30

gives

c_3 = 338.200\ \mathrm{m\,s^{-1}}

N=60

gives

c_2 = 340.600\ \mathrm{m\,s^{-1}}

N=120

gives

c_1 = 339.850\ \mathrm{m\,s^{-1}}

(subscript 1 is the finest grid). ((a)) Compute the successive differences

c_3-c_2

and

c_2-c_1

. ((b)) What does the formula for the observed order

\hat p

give for these values? May a three-grid

\mathrm{GCI}_{\rm fine}

with

F_s=1.25

be reported for

c_1

? ((c)) State what the study should do next before any numerical uncertainty is quoted.

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