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

Locally implicit total variation diminishing schemes on mixed quadrila teral-triangular static/dynamic meshes have been developed to study st eady and unsteady flows, respectively. In a Cartesian coordinate syste m, the Euler equations are solved by using a cell-centered finite volu me algorithm. For steady inviscid flows, the efficiency and accuracy o f the present approach are confirmed by investigating the oblique shoc k 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 quali ty, is presented in this paper. For analyzing the unsteady transonic f low around an NACA 0012 airfoil that pitches harmonically about the qu arter chord, a quadrilateral-triangular dynamic mesh system is used. T he calculated instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with related numer ical and experimental data.