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1. An application of Gaussian process modeling for high-order accurate adaptive mesh refinement prolongation

   Reeves, Steven I. ; Lee, Dongwook ; Reyes, Adam ; Graziani, Carlo ; Tzeferacos, Petros ( October 2021 , Communications in applied mathematics and computational science)

   Bell, John (Ed.)

   We present a new polynomial-free prolongation scheme for Adaptive Mesh Re- finement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based Gaussian Process (GP) prolongation model. The formulation for this scheme was inspired by the two previous studies on the GP methods in- troduced by A. Reyes et al., Journal of Scientific Computing, 76 (2017), and Journal of Computational Physics, 381 (2019). In this paper, we extend the previous GP interpolations and reconstructions to a new GP-based AMR pro- longation method that delivers a third-order accurate prolongation of data from coarse to fine grids on AMR grid hierarchies. In compressible flow simulations, special care is necessary to handle shocks and discontinuities in a stable man- ner. To meet this, we utilize the shock handling strategy using the GP-based smoothness indicators developed in the previous GP work by A. Reyes et al. We compare our GP-AMR results with the test results using the second-order linear AMR method to demonstrate the efficacy of the GP-AMR method in a series of test suite problems using the AMReX library, in which the GP-AMR method has been implemented. 

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2. A high‐order PIC method for advection‐dominated flow with application to shallow water waves

   https://doi.org/10.1002/fld.4506  

   Wang, W. ; Kelly, D. M. ( April 2018 , International Journal for Numerical Methods in Fluids)

   A hybrid Eulerian‐Lagrangian particle‐in‐cell–type numerical method is developed for the solution of advection‐dominated flow problems. Particular attention is given over to the high‐order transfer of flow properties from the particles to the grid. For smooth flows, the method presented is of formal high‐order accuracy in space. The method is applied to solve the nonlinear shallow water equations resulting in a new, and novel, shock capturing shallow water solver. The approach is able to simulate complex shallow water flows, which can contain an arbitrary number of discontinuities. Both trivial and nontrivial bottom topography is considered, and it is shown that the new scheme is inherently well balanced, exactly satisfying the‐property. The scheme is verified against several one‐dimensional benchmark shallow water problems. These include cases that involve transcritical flow regimes, shock waves, and nontrivial bathymetry. In all the test cases presented, very good results are obtained.

    

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3. Eulerian-Eulerian Description of the Interaction of a Shock With Particles Through Godunov’s Scheme

   https://doi.org/10.1115/FEDSM2013-16567  

   Truong, Quang ; Shotorban, Babak ; Jacobs, Gustaaf B. ( January 2013 , The ASME 2013 Fluids Engineering Division Summer Meeting)

   This paper is on an Eulerian-Eulerian (EE) approach that utilizes Godunov’s scheme to deal with a running shock that interacts with a cloud of particles. The EE approach treats both carrier phase (fluid phase) and dispersed phase (particle phase) in the Eulerian frame. In this work, the fluid equations are the Euler equations for the compressible gas while the particle equations are based on a recently developed model to solve for the number density, velocity, temperature, particle sub-grid scale stresses, and particle sub-grid scale heat fluxes. The carrier and dispersed phases exchange momentum and heat, which are modeled through incorporating source terms in their equations. Carrier and dispersed phase equation form a hyperbolic set of differential equations, which are numerically solved with Godunov’s scheme. The numerical solutions are obtained in this work for a two-dimensional normal running shock interacting with a rectangular cloud of particles. The results generated by the EE approach were compared against the results that were generated by a well-stablished Eulerian-Lagragian (EL) approach that treats the carrier phase in an Eulerian frame, while does the dispersed phase in a Lagrangian framework where individuals particles are traced and solved. For the considered configuration, the EE approach reproduced the EL results with a very good accuracy. 

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4. Investigation of the evaporation and fuel property effect on liquid jets in supersonic crossflow

   Zou, Shufan ; Zhou, Dezhi ; Yang, Suo. ( May 2021 , 12th U.S. National Combustion Meeting)

   null (Ed.)

   Due to the longer auto-ignition time with liquid fuels compared with hydrogen, the understanding of interaction of shock waves with sprays and the subsequent vapor mixing is significant to design ramjets/scramjets with liquid fuel sprays. In this study, an Eulerian-Lagrangian framework is developed based on the OpenFOAM platform. In this solver, detailed multi-component transport models for Eulerian gas-phase species properties are included. In addition, Lagrangian spray break-up, atomization and evaporation models are added to simulate liquid phase. In addition, an equilibrium wall function is added to model the near-wall properties. The newly developed solver is used to conduct large eddy simulations (LES) on non-reactive liquid jets in supersonic crossflow (JISCF) with liquid sprays. The liquid penetration length are compared with the experimental data, showing a very good agreement. Effects of evaporation and fuel properties (e.g., heat capacity and enthalpy of evaporation) on penetration length, temperature, Sauter mean diameter (SMD) and volumetric parcel flux are discussed in this study. It is shown that evaporation effects primarily show up in the temperature field. For n-heptane sprays, such impact could be conducted to other properties of the flow field like spray plume size, particle size distribution and volumetric flux, which is caused by the smaller enthalpy of evaporation and heat capacity comparing to water. Full version of this paper has been published as a journal article: Shufan Zou, Dezhi Zhou, Suo Yang, “Effects of Evaporation and Fuel Properties on Liquid Jets in Supersonic Crossflow: a Computational study using a compressible Eulerian-Lagrangian solver”, Atomization and Sprays 30 (9) (2020) 675-696. https://doi.org/10.1615/AtomizSpr.2020034860 

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5. A Spectral/hp-Based Stabilized Solver with Emphasis on the Euler Equations

   https://doi.org/10.3390/fluids9010018  

   Ranjan, Rakesh ; Catabriga, Lucia ; Araya, Guillermo ( January 2024 , Fluids)

   The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries.

    

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