Simulation of the viscous flow past a cylinder with a discontinuous Galerkin spectral element method on a hierarchical Cartesian mesh with adaptive mesh refinement (AMR). The polynomial degree is N = 3 and the mesh uses five refinement levels. The cylinder boundary is imposed with an immersed boundary method (IBM) based on volume penalization [1], which adds a source term to the compressible Navier-Stokes equations,
\n$$
\n\\partial_t \\mathbf{u} + \\nabla \\cdot \\vec{\\mathbf{f}} (\\mathbf{u},\\nabla \\mathbf{u}) = \\underbrace{\\beta (\\mathbf{u}_s – \\mathbf{u})}_{\\text{IBM source}},
\n$$
\nwhere $\\mathbf{u}$ is the vector of conservative quantities, $\\vec{\\mathbf{f}}$ is the Navier-Stokes flux, $\\beta$ is the penalty parameter, and $\\mathbf{u}_s$ is an imposed state. For this simulation, $\\mathbf{u}_s$ mimics an isothermal no-slip wall boundary condition.<\/p>\n
The simulation was obtained with the open-source code FLUXO (https:\/\/github.com\/project-fluxo\/fluxo).<\/p>\n
References<\/strong>
\n[1] Kou, J., Joshi, S., Hurtado-de-Mendoza, A., Puri, K., Hirsch, C., & Ferrer, E. (2022). Immersed boundary method for high-order flux reconstruction based on volume penalization. Journal of Computational Physics, 448, 110721.<\/p>\n