Assessment of a Posteriori Positivity-Preserving Limiters for a Modal Discontinuous Galerkin Method Applied to Multicomponent Flows

When computing high-order solutions of compressible multicomponent flows, numerical instabilities at shock waves and material interfaces must be mitigated without compromising accuracy. A widely adopted strategy is the use of a posteriori limiters to enforce physical admissibility at the cell level. In this work, we compare three different approaches: (i) pointwise correction of the solution followed by projection onto the polynomial space, a pragmatic strategy widely used in industrial practice; (ii) a variant of the Zhang and Shu moment limiter, based on the internal energy; and (iii) a more aggressive strategy based on local order reduction to recover positivity. To control spurious oscillations, an artificial-viscosity shock-capturing technique is employed, and pressure is computed via an L2 projection of the ideal-gas equation of state. The three limiting strategies are assessed in several test cases, including Riemann problems with separated components and a multicomponent implosion. The results show that the moment limiter provides the best compromise between efficiency, robustness, and accuracy for multicomponent flows in the context of modal discontinuous Galerkin methods based on hierarchical and orthonormal bases, whereas the pointwise correction fails in the two-dimensional simulations, and the local order-reduction strategy is overly dissipative.