Truncation Error Analysis of the Rotational Form for the Convective Terms in the Navier–Stokes Equation

✍ Scribed by Kiyosi Horiuti; Takao Itami

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 268 KB
• Volume: 145
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1998.6050

✦ Synopsis

The truncation error of the rotational form for the convective terms in the Navier-Stokes equation is examined in the direct numerical simulation (DNS) of the fully developed turbulent channel flow, in which the low-order finite difference method was used for the partial derivatives in the wall-normal direction. An estimate of the truncation error using the Taylor expansion revealed that this truncation error term is comparable to the rotational stress generation term, represented by the nonlinear kmodel in the Reynolds averaged turbulence models, in the governing equations for the Reynolds shear stress and the normal stress due to the Coriolis force term acting in a channel flow rotating about the spanwise axis. The effective angular velocity due to the truncation error term was dependent on the distance from the wall, and the turbulence was reduced on both sides of the walls analogously to the laminarization of turbulence on the suction side of the conventional rotating channel flow. This analogy was further assessed in the DNS of the channel flow rotating with this effective angular velocity. The time development of the wall friction velocity was similar to that obtained using the rotational form.