The construction of schemes of higher orders of accuracy for calculating flows of viscous fluids using B splines

Schemes of higher orders of accuracy are developed for solving Navier-Stokes equations using the spline collocation method. As an example, a calculation is made of a viscous fluid flow in a cavity. A stationary solution is obtained using the finite difference scheme of Godunov with variable directions. Schemes of third and fourth orders of accuracy are examined, and the formulation of boundary conditions and their effects are discussed.