Characteristics finite element methods in computational fluid dynamics The book details multi dimensional upstream bias algorithms for the numerical solution of the Euler and Navier Stokes equations. Several sections derive the Fluid Dynamics equations from fundamental thermo mechanics principles and systematically develops multi dimensional upstream CFD algorithms with finite element procedures and implicit Runge Kutta time integration algorithms. For mesh independence the formulation is developed at the differential equation level before any spatial discretization. This formulation generates non discrete characteristics bias systems that incorporate an intrinsically multi dimensional and infinite directional genuinely upwind dissipation mechanism. A traditional centered discretization of the characteristics bias system then automatically generates consistent and multi dimensional arbitrary mesh upstream discretizations of the Euler and Navier Stokes Equations. TOC:Overview. Governing Equations of Fluid Dynamics. Constitutive and State Equations. State Equations for Reacting Air. Euler and Navier Stokes Systems. Quasi One Dimensional and Free SurfaceFlow Models. Curvilinear Coordinates. Multi Dimensional Characteristics. Non Discrete Acoustics Convection Upstream Bias Formulations. Upstream Bias Controller. Development of CFD Algorithms. Numerical Methods. Finite Elements. Non Linearly Stable Implicit Runge Kutta Time Integrations. Computational Analysis of Incompressible Flows. Numerical Study of Open Channel Flows. CFD Investigation of Compressible Flows