AbstractThe unsteady Euler equations are numerically solved using the finite volume one‐step scheme recently developed by Ron‐Ho Ni. The multiple‐grid procedure of Ni is also implemented. The flows are assumed to be homo‐enthalpic; the energy equation is eliminated and the static pressure is determined by the steady Bernoulli equation; a local time‐step technique is used. Inflow and outflow boundaries are treated with the compatibility relations method of ONERA. The efficiency of the multiple‐grid scheme is demonstrated by a two‐dimensional calculation (transonic flow past the NACA 12 aerofoil) and also by a three‐dimensional one (transonic lifting flow past the M6 wing). The third application presented shows the ability of the method to compute the vortical flow around a delta wing with leading‐edge separation. No condition is applied at the leading‐edge; the vortex sheets are captured in the same sense as shock waves. Results indicate that the Euler equations method is well suited for the prediction of flows with shock waves and contact discontinuities, the multiple‐grid procedure allowing a substantial reduction of t
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