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We introduce a high-order weight-adjusted discontinuous Galerkin (WADG)scheme for the numerical solution of three-dimensional (3D) wave propagationproblems in anisotropic porous media. We use a coupled first-order symmetricstress-velocity formulation. Careful attention is directed at (a) thederivation of an energy-stable penalty-based numerical flux, which offershigh-order accuracy in presence of material discontinuities, and (b) propertreatment of micro-heterogeneities (sub-element variations) in the numericalscheme. The use of a penalty-based numerical flux avoids the diagonalization ofJacobian matrices into polarized wave constituents necessary when solvingelement-wise Riemann problems. Micro-heterogeneities are accurately and stablyincorporated in the numerical scheme using easily-invertible weight-adjustedmass matrices. The convergence of the proposed numerical scheme is proven andverified by using convergence studies against analytical plane wave solutions.The proposed method is also compared against an existing implementation usingthe spectral element method to solve the poroelastic wave equation.

A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities