Presentation of Problems and Discussion of Results

A complete boundary integral formulation for compressible Navier-Stokes equations

“…In 1987, a GAMM-workshop was organized to bring a small number of scientists highly concerned with the numerical solution of the compressible Navier-Stokes equations to calculate the assigned test problems [5] and to compare the results presented by the contributors each other. One of the assigned test problem was external 2D ow around a NACA0012 airfoil with Direchlet body boundary condition at M ∞ = 0:8; Re = 73 and 500, respectively, angles of attack = 10 • .…”

“…One of the assigned test problem was external 2D ow around a NACA0012 airfoil with Direchlet body boundary condition at M ∞ = 0:8; Re = 73 and 500, respectively, angles of attack = 10 • . All the methods used by the contributors in Reference [5] were ÿeld method (ÿnite di erences, ÿnite elements and ÿnite volumes). In order to compare the results given by present complete boundary integral method with the results [6] given in Reference [5] the same test problems are calculated in this paper.…”

“…All the methods used by the contributors in Reference [5] were ÿeld method (ÿnite di erences, ÿnite elements and ÿnite volumes). In order to compare the results given by present complete boundary integral method with the results [6] given in Reference [5] the same test problems are calculated in this paper. One of the contributors [6] in Reference [5] solved the problems by using a new explicit Navier-Stokes code based on a combination of central ÿnite di erencing and rational Rung-Kutta time stepping.…”

Spline-Characteristic Method for Simulation of Convective Turbulence

“…For the rigid boundary Ѩ 2 u n /Ѩn 2 may be (d) We now assign these values to the nodes of compu-nonzero and the velocity and pressure are coupled by the tational grid and project them into the spline-space to boundary condition (17). Gresho [29] argued that a homocalculate the right-hand sides for geneous Neumann boundary condition can be employed for pressure, but the discrepancy in the pressure boundary condition then introduces a spurious numerical boundary…”

“…Pironneau [5] proposed to use the divergence-free elements in D Dt ϭ Ϫ( и ٌ)u ϩ Pr ٌ 2 ϩ Pr и Ra и ٌ ϫ Tẑ (4) the framework of the method of characteristics to model an incompressible flow. A fully implicit, finite-element scheme DT Dt ϭ ٌ 2 T, for the Navier-Stokes equation was outlined in [17]. Boukir et al [10] have employed an Uzawa algorithm to solve the Stokes problem.…”