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Table 2 Comparison of computed Nusselt number Nu and RMS velocity \(V_{{\mathrm{rms}}}\) with benchmark values from Blankenbach et al. [35]\(^{\mathrm{a}}\) and Koglin Jr et al. [36]\(^{\mathrm{b}}\)

From: Mathematical modelling of mantle convection at a high Rayleigh number with variable viscosity and viscous dissipation

Ra Nu \(V_{{\mathrm{rms}}}\)
This work Benchmark This work Benchmark
\(10^4\) 4.884409 \(4.884409^{\mathrm{a}}\) 42.864973 \(42.864947^{\mathrm{a}}\)
\(10^5\) 10.534113 \(10.534095^{\mathrm{a}}\) 193.215527 \(193.21454^{\mathrm{a}}\)
\(10^6\) 21.972563 \(21.972465^{\mathrm{a}}\) 834.004359 \(833.98977^{\mathrm{a}}\)
\(10^7\) 45.638611 \(45.62^{\mathrm{b}}\) 3633.932754