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We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces…

Numerical Analysis · Mathematics 2024-12-20 Eric L. Peters , John A. Evans

In this paper an even higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an…

Numerical Analysis · Mathematics 2020-10-20 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu

Accurate prediction of aerothermal loads in hypersonic flows is critical yet challenging due to the coupling of Shock-Wave/Boundary-Layer Interactions (SBLI) and thermal non-equilibrium. This work presents the development of a…

Fluid Dynamics · Physics 2026-02-10 Xingjian Gao , Hualin Liu , Fengxiang Zhao , Xing Ji

In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is…

Fluid Dynamics · Physics 2025-08-13 Cal J. Rising , Eric J. Ching , Ryan F. Johnson

Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods…

High Energy Astrophysical Phenomena · Physics 2020-12-09 Samuel J. Dunham , Eirik Endeve , Anthony Mezzacappa , Jesse Buffaloe , Kelly Holley-Bockelmann

In this paper, a uniformly high-order discontinuous Galerkin gas kinetic scheme (DG-HGKS) is proposed to solve the Euler equations of compressible flows. The new scheme is an extension of the one-stage compact and efficient high-order GKS…

Numerical Analysis · Mathematics 2025-10-14 Mengqing Zhang , Shiyi Li , Dongmi Luo , Jianxian Qiu , Yibing Chen

The recently proposed discrete unified gas kinetic scheme (DUGKS) is a finite volume method for deterministic solution of the Boltzmann model equation with asymptotic preserving property. In DUGKS, the numerical flux of the distribution…

Fluid Dynamics · Physics 2015-03-26 Lianhua Zhu , Zhaoli Guo , Kun Xu

In this paper, a unified framework for particulate two-phase flow will be presented with a wide range of solid-particle concentration from dilute to dense limit. The two phase flow is simulated by two coupled flow solvers, i.e., the…

Fluid Dynamics · Physics 2022-02-23 Xiaojian Yang , Wei Shyy , Kun Xu

In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from…

Computational Engineering, Finance, and Science · Computer Science 2022-03-01 Chunhua Zhang , Hong Liang , Zhaoli Guo , Lian-Ping Wang

Adjoint-based sensitivity analysis methods are powerful tools for engineers who use flow simulations for design. However, the conventional adjoint method breaks down for scale-resolving simulations like large-eddy simulation (LES) or direct…

High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design…

Fluid Dynamics · Physics 2015-11-24 Chaitanya Talnikar , Qiqi Wang , Gregory M. Laskowski

We present a discrete filter for subgrid-scale (SGS) model, coupled with the discretization corrected particle strength exchange (DC-PSE) method for the simulation of three-dimensional viscous incompressible flow, at high Reynolds flows.…

Fluid Dynamics · Physics 2024-08-13 Anas Obeidat

This paper develops a framework connecting discrete adjoint gradient-error analysis with an optimization method that uses directional error tolerances, and applies it to airfoil shape optimization governed by a conservative full-potential…

Optimization and Control · Mathematics 2026-05-19 Humberto Gimenes Macedo , Luís Felipe Bueno

We present a high-order discontinuous Galerkin (DG) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ADER-DG method with dynamic adaptive…

Computational Physics · Physics 2020-05-18 Lukas Krenz , Leonhard Rannabauer , Michael Bader

As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…

Computational Physics · Physics 2018-11-02 Ole Burghardt , Nicolas R. Gauger

Modeling and simulation of fluid-structure interactions are crucial to the success of aerospace engineering. This work addresses a novel hybrid algorithm that models the close coupling between compressible flows and deformable materials…

Computational Physics · Physics 2025-04-16 Mingshuo Han , Shiwei Hu , Tianbai Xiao , Yonghao Zhang

The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact…

Numerical Analysis · Mathematics 2025-03-07 Jiawang Zhang , Xing Ji , Kun Xu

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Numerical Analysis · Mathematics 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

We train active neural-network flow controllers using a deep learning PDE augmentation method to optimize lift-to-drag ratios in turbulent airfoil flows at Reynolds number $5\times10^4$ and Mach number 0.4. Direct numerical simulation and…

Fluid Dynamics · Physics 2025-10-09 Xuemin Liu , Tom Hickling , Jonathan F. MacArt

This paper extends the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis acceleration is used in the…

Computational Physics · Physics 2022-11-01 Yue Zhang , Xing Ji , Kun Xu
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