Verification of a viscoelastic fluid flow code by the Method of Manufactured Solution

  • Organista, Juniormar (University of Sao Paulo)
  • Souza, Leandro (University of Sao Paulo)

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In-house numerical codes that are able to simulate fluid flow should be verified to avoid programming errors. There are some ways to check if the code is error-free. This verification becomes harder when the modelling equations are non-linear and do not have an analytical solution. One way to verify this kind of code is through the Method of Manufactured Solution (MMS). This method creates a fictitious solution and allows checks of each code subroutine. In the present work, a numerical code was developed to simulate viscoelastic fluid flow is checked by the MMS. The mathematical model is the two-dimensional Navier-Stokes equations with a viscoelastic model. The viscoelasticity of the fluid is carried out by the Giesekus model. The spatial derivatives are discretized by finite difference schemes. Three codes are adopted, with finite-difference schemes of second, fourth and sixth orders, respectively. A fourth-order Runge-Kutta scheme is adopted for time integration, and a numerical compact filter is used to avoid spurious non-physical oscillations. The MMS adopted is based on sine functions. The results show that the implemented code is error-free, and the order of each code was verified.