This thesis presents a numerical algorithm to simulate viscoelastic fluids in two dimensional problems. The incompressible Navier-Stokes equations, coupled with the multiple mode Giesekus constitutive equation for viscoelastic stress, are used to model viscoelastic fluids in our problem. A second order Godunov method is applied to compute edge-centered, time centered primitive variables as predictors for conservative flux differences, and the correctors are cell-centered conservative variables calculated by applying a conservative update equation including conservative source terms. For the stress equations, we apply a splitting technique which separates the viscoelastic stress into a viscous stress part (elliptic) and an elastic stress part (hyperbolic), and construct an artificial wave speed to slow down the system velocity and increase the CFL stable time step. In addition, the nonlinear stress source term is computed separately by applying an operator splitting method with a new, stable, discretization. This method is second order accurate in time and space, and captures the appropriate viscous and elastic limits. A projection method (BCG method) is used to enforce the velocity incompressibility constraint at edge-centered and cell-centered states. Since there is no longitudinal mode (P-wave mode) in incompressible flow, the double projection method is used to eliminate the longitudinal mode in the extra stress field.
|Advisor:||Miller, Gregory H.|
|Commitee:||Baldis, Hector A., Harris, Walter M.|
|School:||University of California, Davis|
|Department:||Applied Science Engineering|
|School Location:||United States -- California|
|Source:||MAI 49/06M, Masters Abstracts International|
|Subjects:||Applied Mathematics, Mechanical engineering, Plasma physics|
|Keywords:||Giesekus model, Numerical simulation, Viscoelastic flow|
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