A DISSIPATION-FREE TIME-DOMAIN DISCONTINUOUS GALERKIN METHOD APPLIED TO THREE-DIMENSIONAL LINEARIZED EULER EQUATIONS AROUND A STEADY-STATE NON-UNIFORM INVISCID FLOW

2006 ◽  
Vol 14 (04) ◽  
pp. 445-467 ◽  
Author(s):  
MARC BERNACKI ◽  
SERGE PIPERNO
Keyword(s):  
Steady State ◽  
Euler Equations ◽  
Discontinuous Galerkin ◽  
Time Domain ◽  
Balance Equation ◽  
Message Passing ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
General Context ◽  
Linearized Euler Equations

We present in this paper a time-domain discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a nonuniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic energy satisfies a balance equation with source term at the continuous level, and that our numerical framework satisfies an equivalent balance equation at the discrete level and is genuinely dissipation-free. In the case of ℙ1 Lagrange basis functions and tetrahedral unstructured meshes, a parallel implementation of the method has been developed, based on message passing and mesh partitioning. Three-dimensional numerical results confirm the theoretical properties of the method. They include test-cases where Kelvin–Helmholtz instabilities appear.

TIME-DOMAIN PARALLEL SIMULATION OF HETEROGENEOUS WAVE PROPAGATION ON UNSTRUCTURED GRIDS USING EXPLICIT, NONDIFFUSIVE, DISCONTINUOUS GALERKIN METHODS

2006 ◽  
Vol 14 (01) ◽  
pp. 57-81 ◽  
Author(s):  
MARC BERNACKI ◽  
STEPHANE LANTERI ◽  
SERGE PIPERNO
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Wave Energy ◽  
Time Domain ◽  
Balance Equation ◽  
Message Passing ◽  
Heterogeneous Media ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Time Step

A general Discontinuous Galerkin framework is introduced for symmetric systems of conservations laws. It is applied to the three-dimensional electromagnetic wave propagation in heterogeneous media, and to the propagation of aeroacoustic perturbations of either uniform or nonuniform, steady solutions of the three-dimensional Euler equations. In all these linear contexts, the time evolution of some quadratic wave energy is given in a balance equation, with a volumic source term for aeroacoustics in a nonuniform flow. An explicit leap-frog time scheme along with centered numerical fluxes are used in the proposed Discontinuous Galerkin Time Domain (DGTD) method, in order to achieve a discrete equivalent of the balance equation for the wave energy. The scheme introduced is genuinely nondissipative. Numerical first-order boundary conditions are developed to bound the domain and stability is proved on arbitrary unstructured meshes and discontinuous finite elements, under some CFL-like stability condition on the time step. Numerical results obtained with a parallel implementation of the method based on mesh partitioning and message passing are presented to show the potential of the method.

Time Domain Computation of the Wave-Making Resistance of Ships

2005 ◽  
Vol 49 (02) ◽  
pp. 144-158 ◽  
Author(s):  
F. Kara ◽  
D. Vassalos
Keyword(s):  
Steady State ◽  
Time Domain ◽  
Three Dimensional ◽  
Impulse Response Function ◽  
The Body ◽  
Source Distribution ◽  
Research Centre ◽  
Surface Source ◽  
Calm Water ◽  
Marine Engineering

The Ship Stability Research Centre, Department of Naval Architecture and Marine Engineering, The Universities of Glasgow and Strathclyde, Scotland, UKA linearized three-dimensional potential flow formulation in time domain is applied to calculate wave-making resistance of ships in calm water. Steady-state perturbation potentials for resistance are obtained as the steady-state limit of the surge radiation impulse response function using the transient free surface source distribution over the body surface. Five different vessels are used to validate the present numerical approximation. The results, including steady-state wave-making resistance, sinkage force, trim moment, and wave profile along the waterline, are compared with other published numerical and experimental results.

scholarly journals Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Yuma Fukushima ◽  
Daisuke Sasaki ◽  
Kazuhiro Nakahashi
Keyword(s):  
Euler Equations ◽  
Complex Geometry ◽  
Time Integration ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Shielding Effect ◽  
Immersed Boundary ◽  
Noise Propagation ◽  
Linearized Euler Equations ◽  
Cartesian Mesh

The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

scholarly journals Analysis of the Calculation of a Plasma Sheath Using the Parallel SO-DGTD Method

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Qian Yang ◽  
Bing Wei ◽  
Linqian Li ◽  
Debiao Ge
Keyword(s):  
Discontinuous Galerkin ◽  
Cross Section ◽  
Time Domain ◽  
Message Passing ◽  
High Speed ◽  
Large Scale ◽  
Message Passing Interface ◽  
Shift Operator ◽  
Plasma Sheath ◽  
Blunt Cone

The plasma sheath is known as a popular topic of computational electromagnetics, and the plasma case is more resource-intensive than the non-plasma case. In this paper, a parallel shift-operator discontinuous Galerkin time-domain method using the MPI (Message Passing Interface) library is proposed to solve the large-scale plasma problems. To demonstrate our algorithm, a plasma sheath model of the high-speed blunt cone was established based on the results of the multiphysics software, and our algorithm was used to extract the radar cross-section (RCS) versus different incident angles of the model.

scholarly journals Parallel Implementation of the SHYFEM Model

2021 ◽  
Author(s):  
Giorgio Micaletto ◽  
Ivano Barletta ◽  
Silvia Mocavero ◽  
Ivan Federico ◽  
Italo Epicoco ◽  
...  
Keyword(s):  
Message Passing ◽  
Message Passing Interface ◽  
Unstructured Grid ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Implicit Time ◽  
Linear System Of Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Sparse Linear System

Abstract. This paper presents the MPI-based parallelization of the three-dimensional hydrodynamic model SHYFEM (System of HydrodYnamic Finite Element Modules). The original sequential version of the code was parallelized in order to reduce the execution time of high-resolution configurations using state-of-the-art HPC systems. A distributed memory approach was used, based on the message passing interface (MPI). Optimized numerical libraries were used to partition the unstructured grid (with a focus on load balancing) and to solve the sparse linear system of equations in parallel in the case of semi-to-fully implicit time stepping. The parallel implementation of the model was validated by comparing the outputs with those obtained from the sequential version. The performance assessment demonstrates a good level of scalability with a realistic configuration used as benchmark.

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