Academia.eduAcademia.edu

Figure 14 – uploaded by laurent guillot

See full PDFdownloadDownload figure
Figure 14. Upper left : test confiuration for the CG-SEM and HDG-SEM coupling. Upper right : snapshot of the velocity norm at time t = 1.5 sec. Lower left and right : velocity components recorded at the receiver located in the HDG domain. The amplified difference between the numerical solution and the CG-SEM reference solution is shown in blue. The difference remains small even after several wave transmissions across the coupling interface.

Figure 14 Upper left : test confiuration for the CG-SEM and HDG-SEM coupling. Upper right : snapshot of the velocity norm at time t = 1.5 sec. Lower left and right : velocity components recorded at the receiver located in the HDG domain. The amplified difference between the numerical solution and the CG-SEM reference solution is shown in blue. The difference remains small even after several wave transmissions across the coupling interface.

Related Figures (20)

where Ay, = nzAz + nyAy +n,A, is simply expressed in terms of the Lamé parameters as
where Ay, = nzAz + nyAy +n,A, is simply expressed in terms of the Lamé parameters as
Figure 1. (a) Elastic-elastic domain decomposition : on the interface Tg, the field © is single-valued while on is double-valued. (b) Acoustic-acoustic domain decomposition : on Typ the field 6, is single- valued while 6 is double-valued. (c) Acoustic-elastic domain decomposition : on Tyg the field 6, is single-valued while the hybrid pressure p and the hybrid traction on are defined on the acoustic and elastic sides respectively. Figure 1. (a) Elastic-elastic domain decomposition : on the interface I's;, the field 6 is single-valued
Figure 1. (a) Elastic-elastic domain decomposition : on the interface Tg, the field © is single-valued while on is double-valued. (b) Acoustic-acoustic domain decomposition : on Typ the field 6, is single- valued while 6 is double-valued. (c) Acoustic-elastic domain decomposition : on Tyg the field 6, is single-valued while the hybrid pressure p and the hybrid traction on are defined on the acoustic and elastic sides respectively. Figure 1. (a) Elastic-elastic domain decomposition : on the interface I's;, the field 6 is single-valued
Figure 2. Riemann problem in the vicinity of an interface point xp € T°
Figure 2. Riemann problem in the vicinity of an interface point xp € T°
Figure 3. Left : Riemann problem associated to discontinuous states of q at the interface. Right : This leads to hybridized versions of the Riemann solvers previously presented by Wilco
Figure 3. Left : Riemann problem associated to discontinuous states of q at the interface. Right : This leads to hybridized versions of the Riemann solvers previously presented by Wilco
Figure 4. Negative characteristic lines used to build (on) part of the resulting vectorial equality, one get
Figure 4. Negative characteristic lines used to build (on) part of the resulting vectorial equality, one get
Figure 5. Positive characteristic curves used to build (o7)3
Figure 5. Positive characteristic curves used to build (o7)3
Figure 6. Negative characteristic curves used to build «~ €, for acoustic-acoustic interface be similarly determined as
Figure 6. Negative characteristic curves used to build «~ €, for acoustic-acoustic interface be similarly determined as
Figure 7. Characteristic lines for an acoustic-elastic interface. Here 7” is the acoustic impedance, and is the scalar counterpart of the elastic 7~ matrix
Figure 7. Characteristic lines for an acoustic-elastic interface. Here 7” is the acoustic impedance, and is the scalar counterpart of the elastic 7~ matrix
the conservativity condition (25) with the weakly imposed Neumann condition on Q7 NT Moreover, results from section 4 allow to express on and # as
the conservativity condition (25) with the weakly imposed Neumann condition on Q7 NT Moreover, results from section 4 allow to express on and # as
stage. The LSERK4 method is implemented as algorithm 1. The coefficients a;, bj, c; are given in Carpenter & Kennedy (1994). Note that ¢”*@ mean
stage. The LSERK4 method is implemented as algorithm 1. The coefficients a;, bj, c; are given in Carpenter & Kennedy (1994). Note that ¢”*@ mean
Figure 8. Lamb’s Test configuration and velocity norm fields at times t = 0.75 sec (top) and t = 2 sec
Figure 8. Lamb’s Test configuration and velocity norm fields at times t = 0.75 sec (top) and t = 2 sec
Figure 9. Lamb’s problem: errors and convergence orders observed. Left: L?-errors for the numerice
Figure 9. Lamb’s problem: errors and convergence orders observed. Left: L?-errors for the numerice
Figure 10. Elastic-acoustic test configuration. The magnitude of the velocity fields are shown a‘
Figure 10. Elastic-acoustic test configuration. The magnitude of the velocity fields are shown a‘
Figure 11. Elastic-acoustic test case : the L?-norm of the velocity error (left) and the estimated orders of convergence (right) are shown for different order of element polynomial approximation N. »ML absorption does not affect the convergence results
Figure 11. Elastic-acoustic test case : the L?-norm of the velocity error (left) and the estimated orders of convergence (right) are shown for different order of element polynomial approximation N. »ML absorption does not affect the convergence results
and elastic-acoustic problems. The symbol (*) means that post-processing has been performed. The authors warn that none of the implementations used here have been seriously opti- DG and HDG decrease with the polynomial order.
and elastic-acoustic problems. The symbol (*) means that post-processing has been performed. The authors warn that none of the implementations used here have been seriously opti- DG and HDG decrease with the polynomial order.
Figure 12. On the left, configuration of the two-layer computational domain, with the localisations of
Figure 12. On the left, configuration of the two-layer computational domain, with the localisations of
Figure 13. Top : time response of the horizontal and vertical components of the displacement at the horizontal line of receivers located within the top layer as obtained with the HDG-SEM method. The direct P-wave (a) can be clearly distinguished, as well as a strong Rayleigh-to-body-wave (d) generated by the free surface curvature. This wave travels at the S-wave speed and can not always be clearly distinguished from the main S-wave in this figure. Bottom : horizontal and vertical velocities recorded at receiver 50 for the HDG-SEM method, together with the error residual when compared with the CG-SEM solution.
Figure 13. Top : time response of the horizontal and vertical components of the displacement at the horizontal line of receivers located within the top layer as obtained with the HDG-SEM method. The direct P-wave (a) can be clearly distinguished, as well as a strong Rayleigh-to-body-wave (d) generated by the free surface curvature. This wave travels at the S-wave speed and can not always be clearly distinguished from the main S-wave in this figure. Bottom : horizontal and vertical velocities recorded at receiver 50 for the HDG-SEM method, together with the error residual when compared with the CG-SEM solution.
Figure 15. Left : Numerical domain for the seismic-infrasonic simulation. Right : vertical evolution
Figure 15. Left : Numerical domain for the seismic-infrasonic simulation. Right : vertical evolution
The complexity of the generated wave field can clearly be observed on the velocity snap-
The complexity of the generated wave field can clearly be observed on the velocity snap-
Figure 17. Top : Schematic representation of the Antilles section studied. Below : three successive 8 CONCLUSION We have presented a HDG-SEM method for solving elastic-acoustic wave propagation in
Figure 17. Top : Schematic representation of the Antilles section studied. Below : three successive 8 CONCLUSION We have presented a HDG-SEM method for solving elastic-acoustic wave propagation in
Related topics:
Discontinuous Galerkin MethodsComputational SeismologySpectral element methodsHybridizable DG methods
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved