Seminars

In scientific research and industry, accurate and conservative methods for free surface analysis are essential. Especially, mass conservation should be attained because of safety concerns. However, nonlinear effects induced by continuously moving domains make this goal particularly difficult to attain. Besides, accurate dynamic response must be captured for the same reasons and credibility of solutions.

This presentation shows the physical and computational guidelines using an Arbitrary Lagrangian Eulerian (ALE) method fundamentally derived from the Reynolds transport theorem to compute unsteady Newtonian flows including fluid interfaces and free surfaces. The calculation accounts for the frequently overlooked nonlinearity effects, which are costly to treat and therefore require a particular treatment in order to allow the use of large time steps and achieve a computationally efficient method.  The Navier-Stokes equations are then solved using a ‘flow-condition-based interpolation’ (FCBI) scheme along with a finite element scheme. The FCBI method uses exponential interpolations derived from the analytical solution of the 1-dimensional advection-diffusion equation in order to account for up-winding effects. The resulting method conserves mass very accurately, and is stable and accurate even when using coarse meshes.

Finally, a 2-dimensional FCBI method with special focus on its application to flow problems in highly nonlinear moving domains featuring interfaces and free surfaces is revisited. An effective and newly developed 3-D FCBI tetrahedral element is also presented in the context of such applications. The 3-D FCBI solution scheme can solve a wide range of flow problems since it can handle highly nonlinear and unsteady flow conditions, even when large mesh distortions occur. Various example solutions are presented to show the effectiveness of the developed solution schemes.