Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method

The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection-dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice-Sheet and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established streamline upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter do not account for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets.

Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity

Spacecraft-parachute designs quite often include “geometric porosity” created by the hundreds of gaps and slits that the flow goes through. Computational fluid–structure interaction (FSI) analysis of these parachutes with resolved geometric porosity would be exceedingly challenging, and therefore accurate modeling of the geometric porosity is essential for reliable FSI analysis. The space–time FSI (STFSI) method with the homogenized modeling of geometric porosity has proven to be reliable in computational analysis and design studies of Orion spacecraft parachutes in the incompressible-flow regime. Here we introduce porosity models and ST computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. The main components of the ST computational framework we use are the compressible-flow ST SUPG method, which was introduced earlier, and the compressible-flow ST Slip Interface method, which we introduce here. The computations we present for a drogue parachute show the effectiveness of the porosity models and ST computational methods.

Large-eddy simulation of decaying isotropic turbulence using the flowfield dependent variation method

Purpose The purpose of this study is to investigate the accuracy and applicability of the Flowfield Dependent Variation (FDV) method for large-eddy simulations (LES) of decaying isotropic turbulence. Design/methodology/approach In an earlier paper, the FDV method was successfully demonstrated for simulations of laminar flows with speeds varying from low subsonic to high supersonic Mach numbers. In the current study, the FDV method, implemented in a finite element framework, is used to perform LESs of decaying isotropic turbulence. The FDV method is fundamentally derived from the Lax–Wendroff Scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the inherent numerical dissipation of FDV contribute to the scheme’s numerical stability and monotonicity. Understanding the role of numerical dissipation that is inherent to the FDV method is essential for the maturation of FDV into a robust scheme for LES of turbulent flows. Accordingly, three types of LES of decaying isotropic turbulence were performed. The first two types of LES utilized explicit subgrid scale (SGS) models, namely, the constant-coefficient Smagorinsky and dynamic Smagorinsky models. In the third, no explicit SGS model was employed; instead, the numerical dissipation inherent to FDV was used to emulate the role played by explicit SGS models. Such an approach is commonly known as Implicit LES (ILES). A new formulation was also developed for quantifying the FDV numerical viscosity that principally arises from the convective terms of the filtered Navier–Stokes equations. Findings The temporal variation of the turbulent kinetic energy and enstrophy and the energy spectra are presented and analyzed. At all grid resolutions, the temporal profiles of kinetic energy showed good agreement with t(−1.43) theoretical scaling in the fully developed turbulent flow regime, where t represents time. The energy spectra also showed reasonable agreement with the Kolmogorov’s k(−5/3) power law in the inertial subrange, with the spectra moving closer to the Kolmogorov scaling at higher-grid resolutions. The intrinsic numerical viscosity and the dissipation rate of the FDV scheme are quantified, both in physical and spectral spaces, and compared with those of the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of the Streamline Upwind/Petrov–Galerkin (SUPG) finite element method are compared. In the initial stages of turbulence development, all three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. It was also observed that the SUPG method is significantly more dissipative than the three LES approaches. Research limitations/implications Just as any computational method, the limitations are based on the available computational resources. Practical implications Solving problems involving turbulent flows is by far the biggest challenge facing engineers and scientists in the twenty-first century, this is the road that the authors have embarked upon in this paper and the road ahead of is very long. Social implications Understanding turbulence is a very lofty goal and a challenging one as well; however, if the authors succeed, the rewards are limitless. Originality/value The derivation of an explicit expression for the numerical viscosity tensor of FDV is an important contribution of this study, and is a crucial step forward in elucidating the fundamental properties of the FDV method. The comparison of viscosities for the three LES cases and the SUPG method has important implications for the application of ILES approach for turbulent flow simulations.