Recently Ram, Geva, and Sadot [J. Fluid Mech. 768, 219-235 (2015)] showed, experimentally, the formation of a secondary Mach stem generated from the reflection of the primary Mach stem in the aerodynamic regime. Such a phenomenon has never been observed, either experimentally or numerically, in the framework of weak acoustic shocks. In this work, the formation of a secondary Mach stem is observed from the reflection of acoustic shock waves on a convex-concave boundary giving rise to a complex five-shock pattern. This study is fully numerical and is based on the numerical solution of a nonlinear acoustic system of equations using a recently developed discontinuous Galerkin solver.