Zur Konstruktion einer numerischen Lösung des Anfangsrandwertproblems für die nichtlinearen Gleichungen von Navier-Stokes. (On the construction of a numerical solution of the initial-boundary value problem for nonlinear Navier-Stokes equations)
Zur Konstruktion einer numerischen Lösung des Anfangsrandwertproblems für die nichtlinearen Gleichungen von Navier-Stokes. (On the construction of a numerical solution of the initial-boundary value problem for nonlinear Navier-Stokes equations)
Summary: We develop an elementary approach for the construction of a numerical solution for the boundary value problem of the nonstationary nonlinear Navier-Stokes equations in bounded domains of \(\mathbb{R}^ 3\). After a suitable time delay in the nonlinear term we discretize the time using Rothe's method. This leads to linear boundary value problems, which can be reduced to integrals and boundary integral equations by methods of potential theory. For the numerical solution of the integral equations a boundary element method of collocation type is used. Our approach includes an approximation theory, an analysis of stability and convergence, and ends up with three-dimensional numerical test calculations.
Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, Rothe's method, Navier-Stokes equations for incompressible viscous fluids, boundary integral equations, Navier-Stokes equations, stability, nonlinear Navier-Stokes equations, boundary element method
Method of lines for initial value and initial-boundary value problems involving PDEs, convergence, Rothe's method, Navier-Stokes equations for incompressible viscous fluids, boundary integral equations, Navier-Stokes equations, stability, nonlinear Navier-Stokes equations, boundary element method