Althoughб-coordinate is one of the most popular methods used in marine and estuarine modeling,it has long suffered from the so-called"steep boundary problem",namely,the PGF problem.In this paper,a new method called the"б-sharpen immersed boundary method"(б-SIBM)is put forward.In this method,the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain.By this,бHбx of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem,which is,in turn,solved by the SIBM.The accuracy and efficiency of theб-sharpen immersed boundary method(б-SIBM)has been showed by both comparative theoretical analysis and classical numerical tests.First,it is shown that theб-SIBM is more effective than the z-level method,in thatб-SIBM needs special treatment only in the steep section,but the z-level method needs the special treatment in each grid note.Second,it is superior to theб-method in that it is not restricted by the density distribution.This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force(PGFE)and their long-term effects on circulation.It can be seen that,as for the maximum erroneous velocity and kinetic energy,the value ofб-SIBM is much less than that of the z-level method and the traditionalб-method.sharpen immersed boundary method(SIBM),immersed boundary method(IBM),direct forcing method,б-coordinate,
