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This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

Sustainable agriculture implies the ability of agro‐ecosystems to remain productive in the long‐term. It is not easy to point out unambiguously whether or not current production systems meet this sustainability demand. A priori thinking would suggest that organic crops are environmentally favourable, but may ignore the effect of reduced productivity, which shifts the potential impact to other parts of the food provision system. The purpose of this paper is to assess the ecological sustainability of conventional and organic leek production by means of life cycle assessment (LCA).

A cradle‐to‐farm gate LCA is applied, based on real farm data from two research centres. For a consistent comparison, two functional units (FU) were defined: 1ha and 1 kg of leek production.

Assessed on an area basis, organic farming shows a more favourable environmental profile. These overall benefits are strongly reduced when the lower yields are taken into account. Related to organic farming it is therefore important that solutions are found to substantially increase the yields without increasing the environmental burden. Related to conventional farming, important potential for environmental improvements are in optimising the farm nutrient flows, reducing pesticide use and increasing its self‐supporting capacity.

The research is a cradle‐to‐farm gate LCA, future research can be expanded to comprise all phases from cradle‐to‐grave to get an idea of the total sustainability of our present food consumption patterns. The research is also limited to the case of leek production. Future research can apply the methodology to other crops.

To date, there is still lack of clear evidence of the added value of organic farming compared to conventional farming on environmental basis. Few studies have compared organic and conventional food production by means of LCA. This paper addresses these issues.