MUMBAI, India, Aug. 24 -- Intellectual Property India has published a patent application (202641098648 A) filed by Ganji Shankar, Assistant Professor Department Of Mathematics, Matrusri Engineering College.; Dr. A. Mythreye, Associate Professor Department Of Mathematics, Stanley College Of Engineering & Technology For Women.; Dr. S. Prasanna Rani, Associate Professor Department Of Mathematics, Government Degree College For Women.; and Dr. P. Mangathai, Associate Professor Department Of Mathematics on August 14, 2026, for An Adaptive Finite Element Framework For Solving Unsteady Navier–stokes Equations With Dynamic Mesh Refinement For Multiphase Fluid Flow Simulation.
Inventors include Ganji Shankar, Assistant Professor Department Of Mathematics; Dr. A. Mythreye, Associate Professor Department Of Mathematics; Dr. S. Prasanna Rani, Associate Professor Department Of Mathematics; and Dr. P. Mangathai, Associate Professor Department Of Mathematics, Anurag University..
The application for the patent was published on August 21, 2026, under issue no. 34/2026.
Abstract: Abstract A finite element framework for simulating unsteady multiphase fluid flow is disclosed, combining a stabilized (SUPG–PSPG) finite element discretization of the incompressible Navier–Stokes momentum and continuity equations with a level-set interface capturing formulation that tracks a fluid–fluid interface and regularizes density and viscosity across it. An a posteriori error estimator, combining a residual based indicator with an interface-gradient-based indicator, is evaluated element wise and used to dynamically refine or coarsen the computational mesh, automatically concentrating resolution near the evolving fluid interface and regions of high flow gradient. Following each mesh adaptation event, velocity, pressure, and level-set fields are transferred to the newly adapted mesh via a conservative projection operator that preserves discrete mass and momentum, and the simulation time step is adaptively updated according to a Courant Friedrichs Lewy condition evaluated on the adapted mesh. In an illustrative embodiment applied to a benchmark rising bubble problem, the invention achieved interface tracking accuracy comparable to a uniformly refined reference mesh while substantially reducing the total number of degrees of freedom over the course of the simulation. The invention provides a computationally efficient, accurate, and conservative framework for unsteady multiphase flow simulation applicable to chemical process engineering, marine and offshore engineering, biomedical micro fluidics, and environmental fluid mechanics applications.
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