Apollo 11 Reloaded: Optimization-based Trajectory Reconstruction

This paper wants to be a tribute to the Apollo 11 mission, that celebrated its 50th anniversary in 2019. By using modern methods based on numerical optimization we reconstruct critical phases of the original mission, and more specifically the ascent of the Saturn V, the translunar injection maneuver that allowed the crew to leave the Earth’s sphere of influence, and the Moon landing sequence, starting from the powered descent initiation. Results were computed by employing pseudospectral methods, and show good agreement with the original post-flight reports released by NASA after the successful completion of the mission

Ascent and Descent Guidance of Multistage Rockets via Pseudospectral Methods

This paper illustrates the trajectory modeling of multistage rockets for both ascent anddescent phases. The computation of solutions is performed by coupling a multiphase optimal-control problem formulation with a transcription performed via Radau pseudospectral meth-ods. Four examples inspired by both historical rockets like the Saturn V, and modern reusablelaunch systems like the Falcon 9 demonstrate the feasibility of the proposed modeling approachfor the rapid prototyping of valid reference solutions

Development and Validation of a Partitioned Fluid-Structure Solver for Transonic Panel Flutter with Focus on Boundary Layer Effects

A partitioned fluid-structure coupling code for transonic panel flutter has been developed and validated. The Reynolds-averaged Navier-Stokes equations are solved numerically by means of an implicit finite volume method to account for nonlinear aerodynamics, as there are shock waves and a viscous boundary layer at the panel surface. An implicit finite element formulation of the structural equations as well as a Galerkin solution of the von-Kármán plate equation are employed to solve elastic panel deformations with respect to geometric nonlinearities. A detailed validation process is presented in this paper for high subsonic and low supersonic Mach numbers. This comprises a discussion of available results from literature with the objective to propose a guideline for validation purposes of partitioned panel flutter solvers. Thereupon the code is used for studies on the impact of turbulent boundary layer characteristics on aeroelastic stability boundaries and post-flutter. An evaluation of flutter modes and frequencies in the post-flutter domain as well as a discussion of the corresponding flow phenomena is presented

A Priori Neural Networks Versus A Posteriori MOOD Loop: A High Accurate 1D FV Scheme Testing Bed

In this work we present an attempt to replace an a posteriori MOOD loop used in a high accurate Finite Volume (FV) scheme by a trained artificial Neural Network (NN). The MOOD loop, by decrementing the reconstruction polynomial degrees, ensures accuracy, essentially non-oscillatory, robustness properties and preserves physical features. Indeed it replaces the classical a priori limiting strategy by an a posteriori troubled cell detection, supplemented with a local time-step re-computation using a lower order FV scheme (ie lower polynomial degree reconstructions). We have trained shallow NNs made of only two so-called hidden layers and few perceptrons which a priori produces an educated guess (classification) of the appropriate polynomial degree to be used in a given cell knowing the physical and numerical states in its vicinity. We present a proof of concept in 1D. The strategy to train and use such NNs is described on several 1D toy models: scalar advection and Burgers' equation, the isentropic Euler and radiative M1 systems. Each toy model brings new difficulties which are enlightened on the obtained numerical solutions. On these toy models, and for the proposed test cases, we observe that an artificial NN can be trained and substituted to the a posteriori MOOD loop in mimicking the numerical admissibility criteria and predicting the appropriate polynomial degree to be employed safely. The physical admissibility criteria is however still dealt with the a posteriori MOOD loop. Constructing a valid training data set is of paramount importance, but once available, the numerical scheme supplemented with NN produces promising results in this 1D setting. Keywords Neural network • Machine learning • Finite Volume scheme • High accuracy • Hyperbolic system • a posteriori MOOD. Mathematics Subject Classification (2010) 65M08 • 65A04 • 65Z05 • 85A2