Algebraic approximation of sub-grid scales for the variational multiscale modeling of transport problems

摘要: Abstract Variational Multiscale (VMS) Finite Element Methods (FEMs) are robust for the development of general formulations solution multiphysics and multiscale transport problems. To obtain a tractable computationally efficient model, VMS methods often rely on residual-based algebraic approximation sub-grid scales (small or unresolved features field not captured by discretization) using so-called intrinsic time matrix, which depends problem’s overall differential operator represents main model parameter. A novel technique approximating matrix generic problems in relatively inexpensive manner (e.g., does eigenvalue computations) is presented. The method denoted Transport-Equivalent Scaling (TES) based monolithic casting problem as system transient–advective–diffusive–reactive (TADR) equations subsequent scaling coefficient matrices such to preserve each type flux. An formulation incorporating TES complemented with discontinuity-capturing (DC) approach implemented within FEM solver TADR global discrete accomplished generalized-alpha time-stepper together globalized inexact Newton–Krylov nonlinear solver. effectiveness verified simulation benchmark incompressible, compressible, magnetohydrodynamic flow results demonstrate that seamlessly handles incompressible–compressible flows unified without assessing compressibility flow). convergence process more standard scales, well effect DC approach, also investigated. Analysis one-dimensional incompressible reveals similitudes differences between other conventional methods.