This book, Volume 4 of the book series of the Body and Soul mathematics
education reform program, presents a unified new approach to
computational simulation of turbulent flow starting from the general
basis of calculus and linear algebra covered in Volumes 1 through 3. The
book puts the Body and Soul computational finite element methodology in
the form of General Galerkin (G2) up against the challenge of computing
turbulent solutions of the inviscid Euler equations and the
Navier-Stokes equations with small viscosity. It shows that direct
application of G2 without any turbulence or wall modeling, allows
reliable computation on a PC of mean value quantities of turbulent flow
such as drag and lift. The text presents new aspects of both mathematics
and computation of turbulent flow, and challenges established
approaches.