Implicit Time Integration for Scale-Resolving Simulations with Pair-Based Finite-Volume Methods on Unstructured Meshes

Scale-resolving fluid dynamics simulations require fine grids and high-order numerical schemes. For these applications, explicit time integration is usually employed, which severely limits the time step size. Although implicit time integration schemes can have favorable stability properties and allow for larger time steps, they are often overlooked due to their higher computational cost. Implicit schemes are instead commonly used in steady-state simulations, where low-order discretizations are preferred. This work explores the use of state-of-the-art high-order implicit temporal schemes with high-order spatial methods on unstructured grids. Advection and diffusion test cases demonstrate notable mesh convergence rates even with large time steps. An advection-diffusion-reaction numerical benchmark, representative of a spherical flame, is introduced and shows improved accuracy with advanced implicit schemes. Diagonally implicit Runge-Kutta methods, in particular, offer a significant gain in cost-accuracy trade-off over explicit methods, especially in diffusion-driven scale-resolving computations.