5 papers
A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations
Biswajit Khara, Suresh Murugaiyan, Makrand Khanwale +1
The Galerkin finite element formulation of the incompressible Navier-Stokes equations presents two principal challenges: maintaining stable velocity-pressure coupling and controlli…
Proximal Galerkin for Phase Field Fracture
Miguel Castillón, Biswajit Khara, Jørgen S. Dokken +3
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of…
A Semi-Implicit Variational Multiscale Formulation for the Incompressible Navier-Stokes Equations via Exact Adjoint Linearization
Biswajit Khara, Suresh Murugaiyan, Suriya Dhakshinamoorthy +3
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an e…
Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples
Biswajit Khara, Robert Dyja, Kumar Saurabh +2
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we ap…
Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization
Biswajit Khara, Kumar Saurabh, Robert Dyja +2
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-squar…