High-fidelity numerical simulation is one of the ultimate goals in computational fluid dynamics and computational mechanics. The pursuit of this goal has been prompted by the increasing demand of predictive scientists and design engineers to obtain simulations that closely imitate real phenomena. In this talk, the combination of two emerging tools will be explored as a promising alternative to perform high-fidelity simulations. The first tool is a parallel implementation of the hybridizable discontinuous Galerkin (HDG) method. The HDG method is a locally conservative, high-order accurate, and unstructured numerical scheme suited to deploy the physical and numerical accuracy required to obtain high-fidelity approximations to solutions of partial differential equations on complex domains. The second tool, a curved mesh generator, is based on the optimization of a regularized measure of the mesh distortion. This method leads to unstructured curved meshes that approximate with high accuracy the geometry determined by the initial CAD surfaces. Thus, the resulting meshes are adequate to perform high-fidelity finite element analysis with the HDG method. Several simulations will be presented to illustrate the encouraging results obtained using the combination of both tools. Specifically, we will see that this combination provides the physical (locally conservative), numerical (high-order accurate), and geometrical (unstructured curved meshes) accuracy required to perform high-fidelity simulations.