Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Abstract

SUMMARYAlmost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non-orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non-orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L 1 errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier-Stokes simulation of a bare-hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds-stress (ARS) turbulence models using CFDShip-Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0 • and 12 • drift angles. Best predictions are observed when coupling a second-order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30 • drift when using TVD2S-ARS coupled with DES.

A mechanistic model of bubble entrainment in turbulent free surface flows

“…The governing equations are discretized using a control volume/finite differences approach on a collocated grid in space. The convection terms are discretized with linear upwind biased or TVD schemes up to fourth order accurate in space (Ismail et al 2010). Diffusion terms use a second-order central discretization while temporal terms are discretized using a second-order backwards scheme.…”

Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant

“…Though linear (up to fourth order) and TVD (second-order) methods are available in CFDShipIowa version 4 [22], a hybrid 2nd-/4th-order biased scheme is used for DES computations. Diffusion terms are discretized using second-order central discretization.…”

Contributions to modeling of bubble entrainment for ship hydrodynamics applications

“…The governing equations are discretized using a control volume/finite differences approach on a collocated grid in space. The convection terms are discretized with linear upwind biased or TVD schemes (Ismail et al 2010).…”

“…Second order upwind biased (Shu 1998) is used for convection. A second order TVD scheme with superbee limiter (Ismail et al 2010) is used for bubble transport.…”

“…Second order in space and time are used for discretization. The total void fraction transport and multigroup number density transport are solved using a TVD scheme with superbee limiter (Ismail et al 2010) to avoid undershoots that can result in unphysical negative void fraction. A second-order upwind linear scheme is used for the liquid momentum.…”