scholarly journals Regional wave propagation using the discontinuous Galerkin method

Solid Earth ◽  
2013 ◽  
Vol 4 (1) ◽  
pp. 43-57 ◽  
Author(s):  
S. Wenk ◽  
C. Pelties ◽  
H. Igel ◽  
M. Käser
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Regional Scale ◽  
Central Italy ◽  
High Order ◽  
Integration Scheme ◽  
Computational Domain ◽  
Dislocation Source ◽  
High Order Derivative ◽  
Dg Method

Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy). We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depth-dependent ak135 velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies.

scholarly journals Regional wave propagation using the discontinuous Galerkin method

2012 ◽  
Vol 4 (2) ◽  
pp. 1129-1164
Author(s):  
S. Wenk ◽  
C. Pelties ◽  
H. Igel ◽  
M. Käser
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Regional Scale ◽  
Central Italy ◽  
High Order ◽  
Integration Scheme ◽  
Computational Domain ◽  
Dislocation Source ◽  
High Order Derivative ◽  
Dg Method

Abstract. We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. The ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy). We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depth-dependent ak135 velocity model in the upper-mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies.

A High-Order Discontinuous Galerkin Method for Coupled Wave Propagation in 1D Elastoplastic Heterogeneous Media

2018 ◽  
Vol 26 (03) ◽  
pp. 1850043
Author(s):  
Simon Chabot ◽  
Nathalie Glinsky ◽  
E. Diego Mercerat ◽  
Luis Fabian Bonilla
Keyword(s):  
Wave Propagation ◽  
Discontinuous Galerkin ◽  
Heterogeneous Media ◽  
Soil Column ◽  
High Order ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Northern Greece ◽  
Dg Method ◽  
Coupled Wave

We propose a nodal high-order discontinuous Galerkin (DG) method for coupled wave propagation in heterogeneous elastoplastic soil columns. We solve the elastodynamic system written in velocity-strain formulation considering simultaneously the three components of motion. A 3D Iwan elastoplastic model for dry soils under dynamic loading is introduced in the DG method (DG-3C) based on centered fluxes and a low storage Runge–Kutta time scheme. Unlike the linear case, the nonlinear material behavior results in coupling effects between different components of motion. We focus on the choice of the numerical flux for nonlinear heterogeneous media and the classical centered flux is well adapted in terms of stability and direct implementation in 3D. Several numerical applications are studied using a soil column with realistic mechanical properties, and considering successively synthetic and borehole seismic recordings recorded at the Volvi test site (northern Greece).

COMPUTATIONAL ASPECTS OF THE DISCONTINUOUS GALERKIN METHOD FOR THE WAVE EQUATION

2008 ◽  
Vol 16 (04) ◽  
pp. 507-530 ◽  
Author(s):  
TIMO LÄHIVAARA ◽  
MATTI MALINEN ◽  
JARI P. KAIPIO ◽  
TOMI HUTTUNEN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Homogeneous Medium ◽  
Polynomial Degree ◽  
Dg Method ◽  
Runge Kutta ◽  
Element Method

The Discontinuous Galerkin (DG) method is a powerful tool for numerically simulating wave propagation problems. In this paper, the time-dependent wave equation is solved using the DG method for spatial discretization; and the Crank–Nicolson and fourth-order explicit, singly diagonally implicit Runge–Kutta methods, and, for reference, the explicit Runge–Kutta method, were used for time integration. These simulation methods were studied using two-dimensional numerical experiments. The aim of the experiments was to study the effect of the polynomial degree of the basis functions, grid density, and the Courant–Friedrichs–Lewy number on the accuracy of the approximation. The sensitivity of the methods to distorted finite elements was also examined. Results from the DG method were compared with those computed using a conventional finite element method. Three different model problems were considered. In the first experiment, wave propagation in a homogeneous medium was studied. In the second experiment, the scattering and propagation of waves in an inhomogeneous medium were investigated. The third experiment evaluated wave propagation in a more complicated domain involving multiple scattering waves. The results indicated that the DG method provides more accurate solutions than the conventional finite element method with a reduced computation time and a lower number of degrees of freedom.

HIGH-ORDER DISCONTINUOUS GALERKIN SOLUTION OF LOW-RE VISCOUS FLOWS

2009 ◽  
Vol 23 (03) ◽  
pp. 309-312
Author(s):  
HONGQIANG LU
Keyword(s):  
Discontinuous Galerkin ◽  
Euler Method ◽  
High Order ◽  
Navier Stokes ◽  
High Order Schemes ◽  
Seidel Method ◽  
Backward Euler ◽  
Dg Method ◽  
Galerkin Solution ◽  
Nonlinear Discrete System

In this paper, the BR2 high-order Discontinuous Galerkin (DG) method is used to discretize the 2D Navier-Stokes (N-S) equations. The nonlinear discrete system is solved using a Newton method. Both preconditioned GMRES methods and block Gauss-Seidel method can be used to solve the resulting sparse linear system at each nonlinear step in low-order cases. In order to save memory and accelerate the convergence in high-order cases, a linear p-multigrid is developed based on the Taylor basis instead of the GMRES method and the block Gauss-Seidel method. Numerical results indicate that highly accurate solutions can be obtained on very coarse grids when using high order schemes and the linear p-multigrid works well when the implicit backward Euler method is employed to improve the robustness.

Application of Positivity-Preserving Discontinuous Galerkin Scheme in Gaseous Detonations

2017 ◽  
Vol 14 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Cheng Wang ◽  
Yong Bi ◽  
Wenhu Han
Keyword(s):  
Numerical Simulation ◽  
Discontinuous Galerkin ◽  
Chemical Reaction ◽  
High Order ◽  
Gaseous Detonation ◽  
Computational Domain ◽  
Positivity Preserving ◽  
2D Euler Equations ◽  
Numerical Computing ◽  
Complicated Geometry

In numerical simulation of gaseous detonation, due to the complexity of the computational domain, negative density and pressure often emerge in high resolution numerical computing, which leads to blow-ups. The paper provides high order discontinuous Galerkin (DG) positivity-preserving scheme for two-dimensional (2D) Euler equations with two-step chemical reaction which preserve positivity of density, pressure and chemical reaction process. A positivity-preserving limiter is added in high order DG scheme without influencing conservation, accuracy and stability. The method is verified by parallel numerical simulations and is approved to be well applied to numerical simulation of gaseous detonation propagation with complicated geometry boundary.

scholarly journals Variations on Hermite Methods for Wave Propagation

2017 ◽  
Vol 22 (2) ◽  
pp. 303-337 ◽  
Author(s):  
Arturo Vargas ◽  
Jesse Chan ◽  
Thomas Hagstrom ◽  
Timothy Warburton
Keyword(s):  
Wave Propagation ◽  
Time Evolution ◽  
Discontinuous Galerkin ◽  
Hermite Interpolation ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Hyperbolic Pdes ◽  
High Order Convergence ◽  
Dg Methods

AbstractHermite methods, as introduced by Goodrich et al. in [15], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [4]. An example illustrates the simplification of this coupling for Hermite methods.

A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

2014 ◽  
Vol 6 (01) ◽  
pp. 135-144 ◽  
Author(s):  
Hongqiang Lu ◽  
Qiang Sun
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Mesh Size ◽  
High Order ◽  
Shock Capturing ◽  
Local Order ◽  
Galerkin Methods ◽  
Numerical Tests ◽  
Dg Method ◽  
Coarse Grids

AbstractIn this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforwardhp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that thehp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

Sign in / Sign up

Export Citation Format

Share Document