Conclusion

This article begins with a brief presentation of the discretization of diffusion and convection-diffusion partial differential equations by the finite volume method on both structured and unstructured meshes. Various situations were considered, including the discretization of stationary problems as well as evolution problems by explicit and implicit schemes, and the case of problems with discontinuous coefficients. This first part then presents various methods for solving the Navier-Stokes equations using prediction-correction schemes implemented on velocity and pressure meshes that are shifted relative to each other, thus avoiding instabilities when solving the discretized equations. It should be noted that finite volume methods for solving the Navier-Stokes equations are relatively simple to implement (apart from managing indices on offset meshes) and are increasingly used in industry....