عنوان سخنرانی: روش مقياس متغير غير خطي براي حل معادلات انتقالي (Nonlinear variational multiscale approach for transport problems)
سخنران: خانم دكتر مهناز مدير خازني، محقق دانشگاه ماساچوست آمريكا
زمان برگزاري: شنبه 30 ديماه
Diverse transport problems, especially those based on fluid flow models, are intrinsically multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the development of instabilities and turbulence. Computational simulations that resolve all scales in these problems are often unfeasible, prompting to coarse-grained simulation strategies in which small-scale features are modeled instead of resolved. Variational Multiscale (VMS) methods, and particularly their extension as residual-based Large-Eddy Simulation (LES) approaches, have proven effective and robust for the coarse-grained simulation of complex transport problems, particularly turbulent incompressible flows. VMS methods avoid main assumptions in traditional LES, such as separable nonlinearity and empirical small-scale models, by using a variational decomposition of scales together with a residual-based approximation of the small-scales. A nonlinear VMS approach, denoted as VMSn, is presented for the coarse-grained simulation of transient-advective-diffusive-reactive (TADR) transport problems. In contrast to classical VMS approaches that neglect the effect of the small scales on the transport operator, VMSn addresses the inter-dependence between large- and small-scales upfront. The treatment of inter-scale coupling involves the solution of a local algebraic nonlinear system describing the evolution of the small-scales. Two algebraic approximations of the small-scales are investigated: one that uses the main diagonal of the transport operator, suitable for diagonal-dominant problems, and another denoted as Transport-Equivalent Scaling, which is suitable for generic TADR systems. The effectiveness of the VMSn approach is evaluated with benchmark two- and three-dimensional incompressible, compressible, and magnetohydrodynamic laminar flow problems, the incompressible Taylor-Green vortex flow, and the turbulent free jet. Simulation results show that VMSn leads to minor improvements in accuracy with respect to a classical VMS approach for laminar flow problem, but to significantly greater accuracy for the turbulent flow cases. Furthermore, VMSn produces results that are comparable to those using the dynamic Smagorinsky method, the dominant LES approach for incompressible turbulent flows, while presenting a consistent and complete strategy for the handling of generic transport problems.