Utility of the second-order discontinuous Galerkin solvers for environmental modelling applications

Abstract

Accurate reproduction of hydrodynamic and solute mixing processes within cylinder arrays is vital for many environmental modelling applications. Traditional approaches use a second-order finite volume (FV2) method to solve the two-dimensional (2D) planar Reynolds-Averaged Navier-Stokes (RANS) equations and the advection diffusion equation (ADE) to simulate both flow hydrodynamic and solute concentration fields. However, FV2‑based RANS solvers need fine mesh resolutions around the cylinders, resulting in impractical computational costs for large‑scale applications. This study demonstrates the utility of an alternative coarser resolution approach: second-order discontinuous Galerkin (DG2) based solvers of both the shallow water equations (SWE) and the ADE compared to FV2-based RANS and ADE solvers (CFD software) on meshes using much finer resolutions. Results show that these DG2‑based solvers competitively simulate flow hydrodynamic and solute concentration fields at 10 times coarser resolution in the vicinity of cylinders than with the FV2‑based RANS and ADE simulators (ANSYS Fluent). These DG2-based solvers may be a useful alternative to CFD software to support large/field-scale studies where resolution and computational needs are major constraints.