arXiv subjects

Makrand Khanwale

Publications and source records attributed to Makrand Khanwale.

3 recordsLinked to original sources

arXiv2026

A Semi-Implicit Variational Multiscale Formulation for the Incompressible Navier-Stokes Equations via Exact Adjoint Linearization

A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier-Stokes equations. The convection term is linearized using an extrapolated (Oseen-type) convecting velocity, producing a linear advection operator whose adjoint can be written exactly. Because of this exact adjoint, unresolved-scale contributions enter the weak form without spatial derivatives of the fine-scale velocity, thereby eliminating the case-by-case adjustments that often accompany nonlinear residual-based VMS implementations. The formulation is presented for a generalized linear convection operator encompassing the convective, skew-symmetric, and divergence forms. Since the discrete method is linear by construction and monolithic for velocity and pressure, each time step requires only one linear solve, reducing wall-clock time by a factor of $2$ to $5$ relative to fully implicit nonlinear formulations while maintaining comparable accuracy. Temporal convergence is verified, and validation is performed on the lid-driven cavity, flow past a cylinder, turbulent channel flow, and flow over a NACA0012 airfoil at a high Reynolds number, demonstrating the efficiency of the proposed approach on problems of practical scale.

physics.flu-dyn↗

arXiv2026

A Helmholtz-Leray projection method with variational multiscale stabilization for the Navier-Stokes equations

The Galerkin finite element formulation of the incompressible Navier-Stokes equations presents two principal challenges: maintaining stable velocity-pressure coupling and controlling instability in advection-dominated regimes. Moreover, the monolithic formulation produces a coupled nonlinear saddle-point problem. In this work, we present a residual-based variational multiscale (VMS) stabilization of an incremental Helmholtz-Leray projection method that replaces this coupled saddle-point problem with a nonlinear velocity predictor, a pressure Poisson equation, and a velocity projection. The multiscale decomposition is applied only to the predicted velocity; neither the pressure nor the corrected, weakly divergence-free velocity is decomposed into coarse and fine scales. The modeled velocity fine scale contributes consistently to all three subproblems, introducing SUPG-like stabilization in the momentum predictor and a PSPG-like residual contribution in the pressure Poisson equation. We provide a formal error decomposition that separates the BDF2 time-discretization, projection-splitting, and spatial-VMS errors and, under stated stability and spatial-approximation assumptions, yields a combined velocity error estimate with second-order temporal accuracy. Numerical results for manufactured solutions, lid-driven cavity flow, flow past a cylinder, and the Taylor-Green vortex agree closely with established reference data. Comparisons with monolithic VMS indicate that omitting the pressure fine scale reduces drag overprediction and excess modeled dissipation, at the cost of increased divergence error. In the Taylor-Green tests, the projection formulation also reduces the average solution time per step by factors ranging from approximately $1.3\times$ to $2.7\times$ under identical solver settings.

math.NA↗

arXiv2026

An LES model with finite-rate phase change and subgrid spray based on a thermodynamically consistent four-equation multiphase model

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $Σ$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $Σ$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

physics.flu-dyn↗