Space-Time-Parallel Poroelasticity Simulation

TL;DR

This paper presents a space-time variational approach for simulating complex multi-physics processes in heterogeneous porous media, emphasizing stability, accuracy, and efficient parallel implementation for applications in energy, environmental, and biomedical engineering.

Contribution

It introduces a novel space-time variational framework for poroelasticity, including high-order discontinuous time schemes and monolithic multi-physics coupling with advanced preconditioning.

Findings

Developed a stable, high-order space-time discretization method.

Implemented a modular, parallel simulation software DTM++.

Achieved efficient multi-physics coupling with multigrid preconditioning.

Abstract

The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy, environmental, petroleum and biomedical engineering applications fields for instance. Important applications include subsurface compaction drive, carbon sequestration, hydraulic and thermal fracturing and oil recovery. Biomedical applications include the simulation of vibration therapy for osteoporosis processes of trabeculae bones, estimating stress levels induced by tumour growth within the brain or next-generation spinal disc prostheses. Variational space-time methods offers some appreciable advantages such as the flexibility of the triangulation for complex geometries in space and natural local time stepping, the straightforward construction of higher-order approximations and the application of efficient goal-oriented (duality-based) adaptivity concepts. In addition to that, uniform space-time variational methods appear to be advantageous for stability and a priori error analyses of the discrete schemes. Especially (high-order) discontinuous in time approaches appear to have favourable properties due to the weak application of the initial conditions. The development of monolithic multi-physics schemes, instead of iterative coupling methods between the physical problems, is a key component of the research to reduce the modeling error. Special emphasis is on the development of efficient multi-physics and multigrid preconditioning technologies and their implementation. The simulation software DTM++ is a modularised framework written in C++11 and builds on top of deal.II toolchains. The implementation allows parallel simulations from notebooks up to cluster scale.