Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design

Numerical modelling of interfacial soil erosion with viscous incompressible flows

“…[6,21,28]), with a fictitious domain approach (e.g. [7]) in both two and three-dimensional cases (e.g. [25]).…”

Coupling active and passive techniques to control the flow past the square back Ahmed body

“…Let us note that with the L 2 -penalization above there is no numerical boundary layer at order zero contrarily to the H 1 -penalization [1]. There is a numerical boundary layer at order one and if the normal derivative is required at the interface it is possible to improve the method as shown in [11]. The only drawback is the fact that the body has not exactly the real size as it does not fit the mesh.…”

Topology optimization study of arterial bypass configurations using the level set method

“…Challis and Guest (Challis and Guest 2009) studied the topology optimization of twodimensional and three-dimensional Stokes flows by a level set based topology optimization method in which the unwanted degrees of freedom are removed from the matrix system to implement the no-slip condition directly on a fixed mesh in the flow analysis procedure. Chantalat and Bruneau (Chantalat et al 2009) implemented the inverse and shape optimization problems for Stokes flows on uniform Cartesian meshes by integrating the penalization and level set methods. and Kreissl et al (Kreissl et al 2011) discussed the topology optimization of flow domains using a parametric level-set approach in which a lattice Boltzmann method is adopted to predict the flow field.…”