LOCALLY IMPLICIT TOTAL VARIATION DIMINISHING SCHEMES ON MIXED QUADRILATERAL-TRIANGULAR MESHES

Locally implicit total variation diminishing schemes on mixed quadrilateral-triangular static/dynamic meshes have been developed to study steady and unsteady flows, respectively. In a Cartesian coordinate system, the Euler equations are solved by using a cell-centered finite volume algorithm. For steady inviscid flows, the efficiency and accuracy of the present approach are confirmed by investigating the oblique shock reflection at a wall and transonic flow around an NACA 0012 airfoil. To treat unsteady flow problems with moving boundaries, a new dynamic mesh algorithm, which saves memory, is efficient, and maintains quality, is presented in this paper. For analyzing the unsteady transonic flow around an NACA 0012 airfoil that pitches harmonically about the quarter chord, a quadrilateral-triangular dynamic mesh system is used. The calculated instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with related numerical and experimental data.