On the steady solution of non-linear advection equations in steady recirculating flows Original Research Article

Many physical problems like short fiber suspensions flows or viscoelastic flows are modeled by linear and non-linear advection equations. Many of the experimental and industrial flows show often steady recirculating areas which introduce some additional difficulties in the numerical simulation. Actually, the advection equation is supposed to have a steady solution in these steady recirculating flows but neither boundary conditions nor initial conditions are known in such flows. In this paper, we present accurate techniques to solve non-linear advection equations defined in steady recirculating flows. These techniques combine a standard treatment of the non-linearity with a more original treatment of the associated linear problems.