T. Y. Hou’s scientific contributions

... This comes at the price of reducing the accuracy of the scheme unless special techniques are used. Within this family of methods, we mention, for instance, the level set method [42,24], the immersed boundary method [40,41], the fictitious domain approach [34,33], the immersed boundary-conformal isogeometric method [44], the shifted boundary method [39,6], the virtual element method on polygonal pixel-based tessellations [11], the fat boundary method [10] and, finally, the Nitsche-XFEM method [1,19]. ...

Reference:

On the stability and conditioning of a fictitious domain formulation for fluid-structure interaction problems

... The main issue associated with this approach is the problem of maintaining the signed-distance property of the color function: specific advection schemes [23,126,127] and reinitialization of the color function are required [62,70,[128][129][130]. During the reinitialization process the mass of each phase is not conserved and mass losses may occur; while a finer grid may mitigate this issue [125,131], discrete mass conservation for each phase is still not granted [32]. ...

Reference:

Turbulent Flows With Drops and Bubbles: What Numerical Simulations Can Tell Us—Freeman Scholar Lecture