Unified Riemann solution for multi-physics coupling: Anisotropic poroelastic/elastic/fluid interfaces

Abstract For wave propagation problems, we derive a closed expression of Riemann solvers for the interface between two distinct physics models with anisotropic material properties. For the interface coupling of anisotropic poroelastic/elastic/fluid media, the difficulty may arise from two aspects, including (1) different variable numbers from different physics regions and (2) the anisotropy-induced complexity. Fortunately, with a generalized wave impedance, the Riemann problems can be unifiedly solved in a compact and consistent way. The proposed Riemann solution plays a pivotal role for the discontinuous Galerkin time domain method, applied to wave propagation modeling in coupled poroelastic/elastic/fluid media. Numerical results are verified and validated with analytical solution and independent numerical solvers. Finally, we apply our algorithm to solve large-scale wave propagation in a fluid-infilled borehole configuration with heterogeneous poroelastic/elastic formations.

[1]  Georg Stadler,et al.  A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media , 2010, J. Comput. Phys..

[2]  Qing Huo Liu,et al.  The PSTD algorithm: A time-domain method requiring only two cells per wavelength , 1997 .

[3]  Q. Liu,et al.  A new upwind flux for a jump boundary condition applied to 3D viscous fracture modeling , 2018 .

[5]  Georg Stadler,et al.  Scalable adaptive mantle convection simulation on petascale supercomputers , 2008, HiPC 2008.

[6]  Qing Huo Liu,et al.  A three‐dimensional finite difference simulation of sonic logging , 1996 .

[7]  Qing Huo Liu,et al.  A Staggered Upwind Embedded Boundary (SUEB) method to eliminate the FDTD staircasing error , 2004 .

[8]  J. Alvarez,et al.  3-D Discontinuous Galerkin Time-Domain Method for Anisotropic Materials , 2012, IEEE Antennas and Wireless Propagation Letters.

[9]  Jiefu Chen,et al.  Hybridizing semianalytical and conventional finite-element schemes for simulations of electromagnetic borehole resistivity measurement , 2017 .

[10]  Emil M. Constantinescu,et al.  Multiphysics simulations , 2013, HiPC 2013.

[11]  Qing Huo Liu,et al.  A Compact Upwind Flux With More Physical Insight for Wave Propagation in 3-D Poroelastic Media , 2018, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Julien Diaz,et al.  Analytical Solution for Wave Propagation in Stratified Poroelastic Medium. Part II: the 3D Case , 2008, 0807.3864.

[13]  W. Han,et al.  A discontinuous Galerkin method for seismic wave propagation in coupled elastic and poroelastic media , 2019, Geophysical Prospecting.

[14]  José M. Carcione,et al.  Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media , 2011 .

[15]  Michael Dumbser,et al.  Discontinuous Galerkin methods for wave propagation in poroelastic media , 2008 .

[16]  H. Küppers,et al.  The elastic constants of the triclinic crystals, ammonium and potassium tetroxalate dihydrate , 1970 .

[17]  Q. Liu,et al.  An exact Riemann solver for wave propagation in arbitrary anisotropic elastic media with fluid coupling , 2018 .

[18]  Kevin G. Wang,et al.  Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis , 2018 .

[19]  Qing Huo Liu,et al.  Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm , 1999, IEEE Trans. Geosci. Remote. Sens..

[20]  T. Mukerji,et al.  The Rock Physics Handbook , 1998 .

[21]  Todd Arbogast,et al.  A Hybridized Discontinuous Galerkin Method for A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures , 2018, Computer Methods in Applied Mechanics and Engineering.

[22]  Kenneth Duru,et al.  A new discontinuous Galerkin spectral element method for elastic waves with physically motivated numerical fluxes , 2018, 1802.06380.

[23]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers , 2009 .

[24]  Kevin G. Wang,et al.  Shock-Induced Damage and Dynamic Fracture in Cylindrical Bodies Submerged in Liquid. , 2019, International journal of solids and structures.

[25]  T. Plona,et al.  Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies , 1980 .

[26]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes — II. The three-dimensional isotropic case , 2006 .

[27]  Qing Huo Liu,et al.  Discontinuous Galerkin Time-Domain Methods for Multiscale Electromagnetic Simulations: A Review , 2013, Proceedings of the IEEE.

[28]  Q. Liu,et al.  Full-anisotropic poroelastic wave modeling: A discontinuous Galerkin algorithm with a generalized wave impedance , 2019, Computer Methods in Applied Mechanics and Engineering.

[29]  Robert B. Haber,et al.  Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact , 2014 .

[30]  Jean-Pierre Vilotte,et al.  A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation , 2018 .

[31]  J. Carcione,et al.  A nodal discontinuous Galerkin finite element method for the poroelastic wave equation , 2019, Computational Geosciences.

[32]  Hiroshi Takenaka,et al.  FDM simulation of seismic-wave propagation for an aftershock of the 2009 Suruga bay earthquake: Effects of ocean-bottom topography and seawater layer , 2012 .

[33]  E. Toro.  Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .

[34]  A discontinuous Galerkin method with a modified penalty flux for broadband Biot's equation , 2017 .

[35]  Robert B. Haber,et al.  Spacetime simulation of dynamic fracture with crack closure and frictional sliding , 2018, Adv. Model. Simul. Eng. Sci..

[36]  Francisco J. Sánchez-Sesma,et al.  A 3D hp‐adaptive discontinuous Galerkin method for modeling earthquake dynamics , 2012 .

[37]  Leszek Demkowicz,et al.  Solution of coupled poroelastic/acoustic/elastic wave propagation problems using automatic hp-adaptivity , 2014 .

[38]  Pierre-Yves Guerder,et al.  A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation. , 2012, The Journal of the Acoustical Society of America.

[39]  N. F. Dudley Ward,et al.  A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case , 2017, J. Comput. Phys..

[40]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[41]  J. D. L. Puente,et al.  Seismic Wave Simulation for Complex Rheologies on Unstructured Meshes , 2008 .

[42]  Omar Ghattas,et al.  Analysis of an hp-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation , 2012, SIAM J. Numer. Anal..

[43]  Adeline Kornelus.  High Order Hermite and Sobolev Discontinuous Galerkin Methods for Hyperbolic Partial Differential Equations , 2017 .

[44]  Qing Huo Liu,et al.  Isotropic Riemann Solver for a Nonconformal Discontinuous Galerkin Pseudospectral Time-Domain Algorithm , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[45]  Ruichao Ye,et al.  A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves , 2015, 1511.00675.

[46]  Qing Huo Liu,et al.  Efficient Ordinary Differential Equation-Based Discontinuous Galerkin Method for Viscoelastic Wave Modeling , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[47]  Maarten V. de Hoop,et al.  A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: Penalty fluxes and micro-heterogeneities , 2020, J. Comput. Phys..

[48]  Qing Huo Liu,et al.  An Improved Subdomain Level Nonconformal Discontinuous Galerkin Time Domain (DGTD) Method for Materials With Full-Tensor Constitutive Parameters , 2017, IEEE Photonics Journal.

[49]  Emilie Blanc.  Time-domain numerical modeling of poroelastic waves : the Biot-JKD model with fractional derivatives , 2013 .

[50]  Q. Liu,et al.  A discontinuous Galerkin method for simulating the effects of arbitrary discrete fractures on elastic wave propagation , 2017 .

[51]  Randall J. LeVeque,et al.  High-Resolution Finite Volume Modeling of Wave Propagation in Orthotropic Poroelastic Media , 2012, SIAM J. Sci. Comput..

[52]  Qing Huo Liu,et al.  Incorporating Full Attenuation Mechanisms of Poroelastic Media for Realistic Subsurface Sensing , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[53]  Qing Huo Liu,et al.  A Higher Order Hybrid SIE/FEM/SEM Method for the Flexible Electromagnetic Simulation in Layered Medium , 2017, IEEE Transactions on Geoscience and Remote Sensing.