Finite Volume Method and Its Applications in Computational Fluid Dynamics

Various numerical techniques have been developed to address multiple problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique used for solving partial differential equations that represent conservation laws by dividing the domain into control volumes and ensuring flux balance at their boundaries. Its conservative characteristics and capability to work with both structured and unstructured grids make it suitable for addressing issues related to fluid flow, heat transfer, and diffusion. This article introduces an FVM for the linear advection and nonlinear Burgers’ equations through a fifth-order targeted essentially non-oscillatory (TENO5) scheme. Numerical experiments showcase the precision and effectiveness of TENO5, emphasizing its benefits for computational fluid dynamics (CFD) simulations.