Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties

The application of pseudo-symplectic Runge–Kutta methods to the incompressible Navier–Stokes equations is discussed in this work. In contrast to fully energy-conserving, implicit methods, these are explicit schemes of order p that preserve kinetic energy to order q, with q > p. Use of explicit methods with improved energy-conservation properties is appealing for convection-dominated problems, especially in case of direct and large-eddy simulation of turbulent flows. A number of pseudo-symplectic methods are constructed for application to the incompressible Navier–Stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations.