Viscous Moment Imbalance in Finite Volume Method

• 1、College of Aeronautics and Astronautics, National University of Defense Technology, Changsha 410073, China

Abstract：The symmetry of constitutive equations is necessary condition of moment balance of fluid. However, some viscous terms of it will be canceled in Navier-Stokes equation, since their resultant force is zero. As a result, the ordinary finite volume method scarcely employs the constitutive equations completely. By this way, the symmetry will be destroyed. The remaining viscous terms exert extra torque on flow field, whose magnitude equals to vortex circulation multiply by viscous coefficient. This will lead to angular momentum loss in swirling field of ordinary Finite Volume Method; moreover, it cannot be alleviated by grid thickening. To solve this problem, a new algorithm is developed as a modification method. By supposing that fluid element cold rotate round its mass center freely, a new angular momentum equation is presented. Later, it is combined together with translational momentum equation as the new algorithm\'s governing equations. The new algorithm is applied in simulations of steady lid-driven flow within a cavity and of unsteady shear flow, and the results are compared with that of ordinary FVM. It shows that: 1 residual moment is found after calculation converged in ordinary FVM, its value will not diminish even if with thicker grid; 2 the new algorithm conserves angular momentum perfectly, thus overcomes the flaw of ordinary FVM effectively; 3 the distributions of velocity field of two algorithms are different; 4 as for unsteady swirling flow, small eddies simulated with the new method have longer duration time.

Keywords： finite volume method Navier-Stokes equation constitutive equations angular momentum equation viscous moment lid-driven cavity flow