A cost-efficient third-order upwind compact scheme with adjustable dissipation for entropically damped artificial compressibility model-based transient incompressible flows

In this article, a cost-efficient explicit third-order upwind compact difference (UCD3) method with adjustable dissipation (EUCD3-AD) is proposed for the two-dimensional (2D) transient incompressible Navier–Stokes equations (INSEs) based on the entropically damped artificial compressibility method. First of all, the averaged UCD3 scheme (AUCD3), which is the averaged results obtained by the upwind and downwind terms in the existing standard UCD3 scheme, is introduced for the first derivatives. Afterward, a new explicit UCD3 scheme with adjustable dissipation (EUCD3-AD) is proposed for the first derivative within a three-point stencil, which have advantage in cost-efficiency and avoid reducing order of accuracy of the standard UCD3. Moreover, an explicit fourth-order compact difference scheme for calculating the second derivative (ESCD4-S) is proposed based on the AUCD3. The proposed EUCD3-AD with adjusted dissipative nature and the AUCD3 for the first derivative are utilized to approximate the convection terms and the pressure gradient and velocity divergence terms, respectively. The ESCD4-S presnted for the second derivative is used to discretize the viscous and diffusion terms in INSEs. For temporal discretization, the third-order total-variation-diminishing Runge–Kutta method is adopted. Finally, numerical validations of the performance of the newly proposed method are conducted with three benchmark problems involving Taylor–Green vortex, doubly periodic shear layer flows, and lid-driven square cavity. Numerical results demonstrate that EUCD3-AD not only preserves the third-order accuracy and overcomes the over numerical dissipation of the standard UCD3 but also greatly improves the computational efficiency in numerical simulation.