feat(cfd): RMS strain rate (L2 deformation rate)#435
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Add FlowSolution::rms_strain_rate(), the root-mean-square rate-of-strain magnitude over the interior cells: rms = sqrt( <|S|^2> ) (1/s) the L2 deformation rate. Since |S|^2 = 2 S_ij S_ij, this is the quantity that sets the viscous dissipation eps = 2*nu*<S_ij S_ij> = nu*<|S|^2>, so it measures how strongly the flow is being strained (and thus dissipating energy). Completes the strain-rate family (at_cell / max / mean / rms), mirroring rms_vorticity (#406). Analytic test rms_strain_rate_is_the_l2_deformation_rate: (a) pure shear u(y)=gamma*y -> |S|=gamma uniformly -> rms=gamma, and since |S|=|omega|=gamma for a pure shear, rms_strain_rate == rms_vorticity (threads rms_vorticity via the grad-u decomposition); (b) solid-body rotation -> rms strain = 0 while rms vorticity = 2*Omega (strain != rotation); (c) non-uniform quadratic shear -> rms >= mean > 0 (Jensen); (d) grid too small for an interior difference -> 0. Pure method on FlowSolution, no lib.rs change. cfd-native 128 lib tests (was 127), cargo clippy --all-targets -D warnings clean.
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Add beam::hollow_circular_polar_second_moment_of_area(outer_diameter, inner_diameter), the polar second moment of a tube/pipe about its axis: J = pi * (D^4 - d^4) / 32 (m^4) For a CIRCULAR tube this polar second moment IS the genuine St-Venant torsion constant (unlike a non-circular section) -- the torsional stiffness of drive-shaft tubing, far stiffer per weight than a solid shaft. Guard mirrors hollow_circular_second_moment_of_area. Analytic test hollow_circular_polar_second_moment_of_area_is_pi_d4_minus_d4_over_32: (a) worked D=0.1, d=0.05 -> J ~= 9.2038e-6 m^4; (b) threads hollow_circular_second_moment_of_area (#435) (non-tautological, perpendicular-axis theorem): J = 2*I_hollow; (c) threads circular_polar_second_moment_of_area (#423) (non-tautological, annulus): J = J(D) - J(d); (d) solid limit: a zero bore is a solid shaft; (e) 0-sentinel guards for D<=0, d>=D, non-finite, negative bore. Re-exported from lib.rs alphabetically in the beam block. valenx-fem 266 lib tests (was 265), cargo clippy --all-targets -D warnings clean.
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What
Adds
FlowSolution::rms_strain_rate()— the root-mean-square rate-of-strain magnitude over the interior cells:// rms = sqrt( <|S|^2> ) (1/s)Why
The L2 deformation rate. Since
|S|^2 = 2 S_ij S_ij, this is the quantity that sets the viscous dissipationeps = 2*nu*<S_ij S_ij> = nu*<|S|^2>, so it measures how strongly the flow is being strained (and dissipating energy). Completes the strain-rate family (at_cell/max/mean/rms), mirroringrms_vorticity(#406) — so vorticity and strain-rate, the two halves ofgrad-u, now each have a full statistic set.Test
rms_strain_rate_is_the_l2_deformation_rate(5x5 unit grid):u(y)=gamma*y->|S|=gammauniformly ->rms=gamma, and since|S|=|omega|=gammafor a pure shear,rms_strain_rate == rms_vorticity(threadsrms_vorticityvia the grad-u decomposition);0while rms vorticity =2*Omega(strain != rotation);rms >= mean > 0(Jensen);0.Pure method on
FlowSolution, nolib.rschange.valenx-cfd-native128 lib tests (was 127);cargo clippy -p valenx-cfd-native --all-targets -- -D warningsclean. Research-grade flow-deformation / dissipation diagnostic.