This study was aimed at assessing the robustness of a fixed-grid fluid-structure interaction method (Multi-Material Arbitrary Lagrangian-Eulerian) to modelling the two-dimensional native aortic valve dynamics and comparing it to the Arbitrary Lagrangian-Eulerian method. For the fixed-grid method, the explicit finite element solver LS-DYNA was utilized, where two independent meshes for the fluid and structure were generated and the penalty method was used to handle the coupling between the fluid and structure domains. For the Arbitrary Lagrangian-Eulerian method, the implicit finite element solver ADINA was used where two separate conforming meshes were used for the valve structure and the fluid domains. The comparison demonstrated that both fluid-structure interaction methods predicted accurately the valve dynamics, fluid flow, and stress distribution, implying that fixed-grid methods can be used in situations where the Arbitrary Lagrangian-Eulerian method fails.