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A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the 'implied' presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation. Numerical experiments of Rayleigh-Bénard convection (RBC) and Rayleigh-Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids; therefore, we consider that the proposed discretization forms an excellent starting point for testing sub-grid scale models.

While the operating cost of electricity grids based on thermal generation was largely driven by the cost of fuel, as renewable penetration increases, ancillary services represent an increasingly large proportion of the running costs. Electric frequency is an important magnitude in highly renewable grids, as it becomes more volatile and therefore the cost related to maintaining it within safe bounds has significantly increased. So far, costs for frequency-containment ancillary services have been socialised in most countries, but it has become relevant to rethink this regulatory arrangement. In this paper, we discuss the issue of cost allocation for these services, highlighting the need to evolve towards a causation-based regulatory framework. We argue that parties responsible for creating the need for ancillary services should bear these costs. However, this would imply an important change in electricity market policy, therefore it is necessary to understand the impact on current and future investments on generation, as well as on electricity tariffs. Here we provide a mostly qualitative analysis of this issue, defining guidelines for practical implementation and further study. Published in journal Energy Policy