In this work, we develop a novel energy-stable linear approach, which we name as auxiliary
variable viscosity splitting (AVVS) method, to efficiently solve the incompressible fluid flows …

We present in this paper a new second-order consistent splitting scheme for the Navier–
Stokes equations with no-slip boundary conditions based on (i) the Taylor expansions at …

We present novel numerical schemes for the incompressible Navier-Stokes equations with
variable density and address two critical concerns, ie, the preservation of lower density …

Abstract The Patlak-Keller-Segel-Navier-Stokes system describes the biological chemotaxis
phenomenon in the fluid environment. It is a coupled nonlinear system with unknowns being …

Viscoelastic fluids are highly challenging from the rheological standpoint, and their
discretization demands robust, efficient numerical solvers. Simulating viscoelastic flows …

Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic
balance (HB) method and its variants have been the most widely‐used approaches for such …

We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar
auxiliary variable (SAV) scheme for Navier–Stokes equation with periodic boundary …

We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent
splitting scheme coupled with a generalized scalar auxiliary variable (GSAV) approach for …

Perturbed rapidly rotating flows are dominated by inertial oscillations, with restricted group
velocity directions, due to the restorative nature of the Coriolis force. In containers with some …

In this paper, we construct two kinds of exponential SAV approach with relaxation (R-ESAV)
for dissipative system. The constructed schemes are linear and unconditionally energy …