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SUMMARY: The 15 January 2022 eruption of the Hunga–Tunga volcano generated a Lamb pressure wave propagating all over the globe and triggering a tsunami throughout the planet. A first atmospheric wave arrived 16 hr after the eruption on the French Mediterranean coasts and propagated southward. A second one originating from Africa was observed 4 hr later with an attenuated amplitude. The first wave can be roughly defined either by a N wave or a sinusoid signal with a period close to 50 min and an amplitude of 130 Pa. In the Mediterranean Sea, the tsunami was recorded by almost all standard coastal tide gauges or pressure gauges. The French tide gauge stations recorded water waves with amplitudes ranging from a few centimetres to 10 cm and with periods ranging from 10 min to 1 hr. Numerical simulation of the tsunami is performed by the operational code Taitoko for different atmospheric sources. Non-linear shallow water equations are solved by a finite-difference method, using the nested multigrid approach. The tsunami is generated by calculating analytically the atmospheric pressure gradient in the momentum equations. Comparisons of time-series between numerical solutions and records are satisfactory for most tide-gauges along the French Mediterranean coast. Sensitivity analysis on the atmospheric source and on the resolution is performed. For most tide-gauge stations, numerical results show that the wave forms depend first on local resonance phenomena. [ABSTRACT FROM AUTHOR]