On the design of high order residual-based dissipation for unsteady compressible flows

none3The numerical dissipation operator of Residual-Based Compact (RBC) schemes of high accuracy is identified and analysed for hyperbolic systems of conservation laws. A necessary and sufficient condition (-criterion) is found that ensures dissipation in 2-D and 3-Dfor any order of the RBC scheme. Numerical applications of RBC schemes of order 3, 5 and 7 to a diagonal wave advection and to a converging cylindrical shock problem confirm the theoretical results.A. Lerat; K. Grimich; P. CinnellaA., Lerat; K., Grimich; Cinnella, Paol

High-order implicit residual smoothing time scheme for direct and large eddy simulations of compressible flows

Restrictions on the maximum allowable time step of explicit time integration methods for direct and large eddy simulations of compressible turbulent flows at high Reynolds numbers can be very severe, because of the extremely small space steps used close to solid walls to capture tiny and elongated boundary layer structures. A way of increasing stability limits is to use implicit time integration schemes. However, the price to pay is a higher computational cost per time step, higher discretization errors and lower parallel scalability. In quest for an implicit time scheme for scale-resolving simulations providing the best possible compromise between these opposite requirements, we develop a Runge–Kutta implicit residual smoothing (IRS) scheme of fourth-order accuracy, based on a bilaplacian operator. The implicit operator involves the inversion of scalar pentadiagonal systems, for which efficient parallel algorithms are available. The proposed method is assessed against two explicit and two implicit time integration techniques in terms of computational cost required to achieve a threshold level of accuracy. Precisely, the proposed time scheme is compared to four-stages and six-stages low-storage Runge–Kutta method, to the second-order IRS and to a second-order backward scheme solved by means of matrix-free quasi-exact Newton subiterations. Numerical results show that the proposed IRS scheme leads to reductions in computational time by a factor 3 to 5 for an accuracy comparable to that of the corresponding explicit Runge–Kutta scheme

Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates

International audienceThe lack of an universal modelling approach for turbulence in Reynolds-Averaged Navier–Stokes simulations creates the need for quantifying the modelling error without additional validation data. Bayesian Model-Scenario Averaging (BMSA), which exploits the variability on model closure coefficients across several flow scenarios and multiple models, gives a stochastic, a posteriori estimate of a quantity of interest. The full BMSA requires the propagation of the posterior probability distribution of the closure coefficients through a CFD code, which makes the approach infeasible for industrial relevant flow cases. By using maximum a posteriori (MAP) estimates on the posterior distribution, we drastically reduce the computational costs. The approach is applied to turbulent flow in a pipe at Re= 44,000 over 2D periodic hills at Re=5600, and finally over a generic falcon jet test case (Industrial challenge IC-03 of the UMRIDA project)

Numerical investigation of dense gas flows through transcritical multistage axial Organic Rankine Cycle turbines

Many recent studies suggest that supercritical Organic Rankine Cycles (ORCs), i.e., ORCs in which heat is supplied at a pressure greater than the liquid/vaport critical point pressure, have a great potential for low-temperature heat recovery applications, since they allow better recovery efficiency for a simplified cycle architecture. In this work we investigate supercritical flows of dense gases through axial, multi-stage, ORC turbines, using a numerical code including advanced equations of state and a high-order discretization scheme. At this stage, we focus on inviscid flow effects due to the peculiar thermodynamic behavior of the working fluids. Bidimensional numerical simulations are carried out, initially for a single stage and then for the complete turbine, for three working fluids: the refrigerants R134a and R245fa and carbon dioxide (CO2). For the last one, the turbine is simulated for both inlet and outlet supercritical conditions. For R134a and R245fa, both supercritical and subcritical inlet turbine conditions are considered, the outlet pressure being always subcritical. Numerical simulations are used to evaluate the turbine adiabatic efficiencies found in the different cases, and an in-detail investigation of the flow field across the turbine is carried out to understand the main loss mechanisms. Shock-wave formation is found to have a crucial impact on the overall performance: carbon dioxide is shown to provide an optimal behavior since, because of the high values of the speed of sound in this fluid, the flow field is completely subsonic and no shock-waves are created. However, carbon dioxide requires to work at pressures of the order of 50 bars, which leads to higher installation costs. The use of R134a ensures satisfactory adiabatic efficiencies, despite the presence of weak shocks at the suction sides of rotor blades, whereas R245fa develops, for the turbine configuration considered in this work, strong shocks leading to significant losses. For both fluids, using supercritical inlet conditions tends to increase turbine isentropic efficiency for a given pressure ratio since, at high pressures, their thermodynamic behavior significantly deviates from that of a perfect gas, slowing down the increase of the Mach number during turbine expansion, and leading to weaker shocks

Development and analysis of high-order vorticity confinement schemes

High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate com- putation of vortical flows, following the VC2 conservative formulation of Steinhoff. First, a high-order formulation of VC is presented for the case of the linear transport equation for decoupled schemes in space and time. A spectral analysis shows that the new nonlinear schemes have improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. For the Euler and Navier–Stokes equations, the original VC method is extended to 3 rd - and 5 th -order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1 st -order method and is suitable for application to high-order numerical simulations. The high-order ex- tensions remain both independent of the choice of baseline numerical scheme and rotationally invariant since they are based on the Laplace operator. Numerical tests validate the increased order of accuracy, vorticity-preserving capability and compatibility of the VC extensions with high-order methods

Development of a third-order accurate vorticity confinement scheme

A new 3rd-order Vorticity Confinement scheme is presented as an extension of the original VC2 scheme developed by Steinhofffor the resolution of the fluid dynamic equations. The theoretical developments are explained, and the method is tested. The results obtained show that the new scheme combines the accuracy of the underlying higher order scheme and the confinement capability of the original VC2 method

Simplex-stochastic collocation method with improved scalability

The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling