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.

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.

scholarly journals Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. T67-T77 ◽  
Author(s):  
Sara Minisini ◽  
Elena Zhebel ◽  
Alexey Kononov ◽  
Wim A. Mulder
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Local Time ◽  
Heterogeneous Media ◽  
Small Scale ◽  
Time Step ◽  
Element Discretization ◽  
Time Stepping ◽  
Local Time Stepping

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than finite-difference methods, but this is compensated by their superior accuracy if the finite-element mesh follows the sharp impedance contrasts and by their improved efficiency if the element size scales with wavelength, hence with the local wave velocity. However, 3D complex geologic settings often contain details on a very small scale compared to the dominant wavelength, requiring the mesh to contain elements that are smaller than dictated by the wavelength. Also, limitations of the mesh generation software may produce regions where the elements are much smaller than desired. In both cases, this leads to a reduction of the time step required to solve the wave propagation and significantly increases the computational cost. Local time stepping (LTS) can improve the computational efficiency and speed up the simulation. We evaluated a local formulation of an LTS scheme with second-order accuracy for the discontinuous Galerkin finite-element discretization of the wave equation. We tested the benefits of the scheme by considering a geologic model for a North-Sea-type example.

A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media

2017 ◽  
Vol 21 (4) ◽  
pp. 1065-1089 ◽  
Author(s):  
Jun Yang ◽  
Wei Cai ◽  
Xiaoping Wu
Keyword(s):  
Discontinuous Galerkin ◽  
Time Domain ◽  
Heterogeneous Media ◽  
Underground Structure ◽  
Three Dimensional ◽  
Low Frequency ◽  
Time Discretization ◽  
High Order ◽  
Basis Functions ◽  
Computational Domain

AbstractWe present a high-order discontinuous Galerkin (DG) method for the time domain Maxwell's equations in three-dimensional heterogeneous media. New hierarchical orthonormal basis functions on unstructured tetrahedral meshes are used for spatial discretization while Runge-Kutta methods for time discretization. A uniaxial perfectly matched layer (UPML) is employed to terminate the computational domain. Exponential convergence with respect to the order of the basis functions is observed and large parallel speedup is obtained for a plane-wave scattering model. The rapid decay of the out-going wave in the UPML is shown in a dipole radiation simulation. Moreover, the low frequency electromagnetic fields excited by a horizontal electric dipole (HED) and a vertical magnetic dipole (VMD) over a layered conductive half-space and a high frequency ground penetrating radar (GPR) detection for an underground structure are investigated, showing the high accuracy and broadband simulation capability of the proposed method.

Nonlinear Time-Domain Simulation of the Heaving-Buoy Type Wave Energy Converter by Using Three-Dimensional Potential Numerical Wave Tank Under Irregular Wave Conditions

2020 ◽  
Author(s):  
Sung-Jae Kim ◽  
Weoncheol Koo ◽  
Moo-Hyun Kim
Keyword(s):  
Wave Energy ◽  
Time Domain ◽  
Three Dimensional ◽  
Wave Energy Converter ◽  
Hydrodynamic Performance ◽  
Numerical Wave Tank ◽  
Energy Converter ◽  
Wave Tank ◽  
Type Wave ◽  
Numerical Wave

Abstract The aim of this paper is to evaluate the hydrodynamic performance of a heaving buoy type wave energy converter (WEC) and power take-off (PTO) system. To simulate the nonlinear behavior of the WEC with PTO system, a three-dimensional potential numerical wave tank (PNWT) was developed. The PNWT is a numerical analysis tool that can accurately reproduce experiments in physical wave tanks. The developed time-domain PNWT utilized the previously developed NWT technique and newly adopted the side wall damping area. The PNWT is based on boundary element method with constant panels. The mixed Eulerian-Lagrangian method (MEL) and acceleration potential approach were adopted to simulate the nonlinear behaviors of free-surface nodes associated with body motions. The PM spectrum as an irregular incident wave condition was applied to the input boundary. A floating or fixed type WEC structure was placed in the center of the computational domain. A hydraulic PTO system composed of a hydraulic cylinder, hydraulic motor and generator was modeled with approximate Coulomb damping force and applied to the WEC system. Using the integrated numerical model of the WEC with PTO system, nonlinear interaction of irregular waves, the WEC structure, and the PTO system were simulated in the time domain. The optimal hydraulic pressure of the PTO condition was predicted. The hydrodynamic performance of the WEC was evaluated by comparing the linear and nonlinear analytical results and highlighted the importance accounting for nonlinear free surfaces.

scholarly journals Simulation of elastic wave propagation across fractures using a nodal discontinuous Galerkin method—theory, implementation and validation

2019 ◽  
Vol 219 (3) ◽  
pp. 1900-1914 ◽  
Author(s):  
T Möller ◽  
W Friederich
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Discontinuous Galerkin ◽  
Heterogeneous Media ◽  
Rheological Behaviour ◽  
Displacement Discontinuity ◽  
Signal Frequency ◽  
Elastic Wave Equation ◽  
Numerical Flux

SUMMARY An existing nodal discontinuous Galerkin (NDG) method for the simulation of seismic waves in heterogeneous media is extended to media containing fractures with various rheological behaviour. Fractures are treated as 2-D surfaces where Schoenberg’s linear slip or displacement discontinuity condition is applied as an additional boundary condition to the elastic wave equation which is in turn implemented as an additional numerical flux within the NDG formulation. Explicit expressions for the new numerical flux are derived by considering the Riemann problem for the elastic wave equation at fractures with varying rheologies. In all cases, we obtain further first order differential equations that fully describe the temporal evolution of the particle velocity jump at the fracture. Our flux formulation allows to separate the effect of a fracture from flux contributions due to simple welded interfaces enabling us to easily declare element faces as parts of a fracture. We make use of this fact by first generating the numerical mesh and then building up fractures by selecting appropriate element faces instead of adjusting the mesh to pre-defined fracture surfaces. The implementation of the new numerical fluxes into NDG is verified in 1-D by comparison to an analytical solution and in 2-D by comparing the results of a simulation valid in 1-D and 2-D. Further numerical examples address the effect of fracture systems on seismic wave propagation in 1-D and 2-D featuring effective anisotropy and coda generation. Finally, a study of the reflective and transmissive behaviour of fractures indicates that reflection and transmission coefficients are controlled by the ratio of signal frequency and relaxation frequency of the fracture.

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.

Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

2016 ◽  
Vol 19 (1) ◽  
pp. 205-225 ◽  
Author(s):  
Jean-Noel G. Leboeuf ◽  
Viktor K. Decyk ◽  
David E. Newman ◽  
Raul Sanchez
Keyword(s):  
Domain Decomposition ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Massively Parallel ◽  
Problem Size ◽  
Time Step ◽  
Particle In Cell ◽  
Minor Radius ◽  
Efficient Charge ◽  
Cartesian Geometry

AbstractThe massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.

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