Book Review: Handbook of numerical analysis, Vol. VI, Numerical methods for solids (Part 3), Numerical methods for fluids (Part 1)

Numerical Methods and Stochastics Part I: Numerical Methods

International Journal for Numerical Methods in Fluids

A numerical technique (FGVT) for solving the time-dependent incompressible Navier–Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity–pressure grid. It also uses a special flux-corrected transport ...

International Journal for Numerical Methods in Fluids

A pulsating laminar flow of a viscous, incompressible liquid in a rectangular duct has been studied. The motion is induced under an imposed pulsating pressure difference. The problem is solved numerically. Different flow regimes are characterized by a non-dimensional parameter based on the frequency (v) of the imposed pressure gradient oscillations and the width of the duct (h). This, in fact, ...

International Journal for Numerical Methods in Fluids

Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) ba...

International Journal for Numerical Methods in Fluids

The weak Lagrange–Galerkin finite element method for the two-dimensional shallow water equations on adaptive unstructured grids is presented. The equations are written in conservation form and the domains are discretized using triangular elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the non-linearities introd...