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Initially he worked in the field of missile aerodynamics and later shifted to CFD and devised the Roe solver for numerical computation of compressible flows with shocks.
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He has developed approximate Riemann solver called Roe solver for compressible flows with shocks.
By the time of his death at almost age 90 in 1972, not even his family or his neighbors in Bad Bevensen, Germany were aware of the formative role he had played, with Ludwig Prandtl, in the scientific discipline known as Compressible flow or Gas dynamics.
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During the first decade of the 20th century, Meyer worked under Prandtl's guidance at the Georg-August-University in Göttingen, Germany on the theory of supersonic gas flows, then a brand-new field of study that we now call Compressible flow or Gas dynamics.