Numerical computation of triangular cavity flows by a Lagrange-Galerkin scheme with a locally linearized velocity

摘要

We show numerical results of triangular cavity flow problems solved by aLagrange-Galerkin scheme free from numerical quadrature. The scheme hasrecently developed by us, where a locally linearized velocity and the backwardEuler approximation are used in finding the position of fluid particle at theprevious time step. Since the scheme can be implemented exactly as it is, thetheoretical stability and convergence results are assured, while theconventional Lagrange-Galerkin schemes may encounter the instability caused bynumerical quadrature errors. The scheme is employed to solve cavity flowproblems in triangular domains, where we observe the bifurcation of stationarysolutions and the patterns of streamlines.