scholarly journals Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes

2015 ◽  
Vol 103 (5) ◽  
pp. 342-363 ◽  
Author(s):  
A. Gargallo-Peiró ◽  
X. Roca ◽  
J. Peraire ◽  
J. Sarrate
Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. T77-T97 ◽  
Author(s):  
Josep de la Puente ◽  
Michael Dumbser ◽  
Martin Käser ◽  
Heiner Igel

We have developed a new numerical method to solve the heterogeneous poroelastic wave equations in bounded three-dimensional domains. This method is a discontinuous Galerkin method that achieves arbitrary high-order accuracy on unstructured tetrahedral meshes for the low-frequency range and the inviscid case. By using Biot’s equations and Darcy’s dynamic laws, we have built a scheme that can successfully model wave propagation in fluid-saturated porous media when anisotropy of the pore structure is allowed. Zero-inflow fluxes are used as absorbing boundary conditions. A continuous arbitrary high-order derivatives time integration is used for the high-frequency inviscid case, whereas a space-time discontinuous scheme is applied for the low-frequency case. We conducted a numerical convergence test of the proposed methods. We used a series of examples to quantify the quality of our numerical results, comparing them to analytic solutions as well as numerical solutions obtained by other methodologies. In particular, a large scale 3D reservoir model showed the method’s suitability to solve poroelastic wave-propagation problems for complex geometries using unstructured tetrahedral meshes. The resulting method is proved to be high-order accurate in space and time, stable for the low-frequency case, and asymptotically consistent with the diffusion limit.


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