MUMBAI, India, July 13 -- Intellectual Property India has published a patent application (202641083712 A) filed by Naikoti Kishan, Professor Department Of Mathematics, Osmania University, Hyderabad.; Dr. Srinivas Maripala, Junior Lecturer Department Of Mathematics, Government Junior College, Yeldurthy, Medak.; and Srinivas Reddy C, Associate Professor Department Of on July 07, 2026, for A Space Time Finite Element Method For Incompressible Navier–stokes Equations With Dynamic Mesh Refinement For Free-Surface Flow.
Inventors include Naikoti Kishan, Professor Department Of Mathematics; Dr. Srinivas Maripala, Junior Lecturer Department Of; and Srinivas Reddy C, Associate Professor Department Of.
The application for the patent was published on July 10, 2026, under issue no. 28/2026.
Abstract: Abstract The present invention discloses a space-time finite element method for solving the incompressible Navier–Stokes equations in domains bounded by a moving free surface, with dynamic mesh refinement. Time is partitioned into space-time slabs over which the coupled velocity and pressure are discretised, with continuity between slabs enforced weakly in a discontinuous Galerkin in time manner and the spatial domain permitted to deform to track the free surface. A stabilized formulation using SUPG, PSPG, and LSIC terms permits equal order interpolation, the kinematic and dynamic free surface conditions are enforced within the formulation, and an error indicator drives local refinement and coarsening of the mesh near the interface and in high gradient regions between successive slabs. The nonlinear system is solved by Newton Raphson iteration with a preconditioned GMRES solver. The method reproduces benchmark free-surface flows with optimal second-order accuracy while attaining target accuracy at a small fraction of the elements, computational time, and memory of a uniform mesh.
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