Discrete adjoint methodology for general multiphysics problems

This article presents a methodology whereby adjoint solutions for partitioned multiphysics problems can be computed efficiently, in a way that is completely independent of the underlying physical sub-problems, the associated numerical solution methods, and the number and type of couplings between them. By applying the reverse mode of algorithmic differentiation to each discipline, and by using a specialized recording strategy, diagonal and cross terms can be evaluated individually, thereby allowing different solution methods for the generic coupled problem (for example block-Jacobi or block-Gauss-Seidel). Based on an implementation in the open-source multiphysics simulation and design software SU2, we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a heat exchanger (conjugate heat transfer), a deforming wing (fluid–structure interaction), and a cooled turbine blade where both effects are simultaneously taken into account.

IMPROVED ANISOTROPIC LINEAR SOURCE FORMULATION FOR MULTIPHYSICS PROBLEMS

This work seeks to extend an existing formulation of the method of characteristics with linear source approximation for problems with dynamic cross sections. The previous formulation eliminated cross section dependence of precomputed coefficients for systems with an isotropic source. The method is extended to include a formulation for spatially flat anisotropic scattering that eliminates cross section dependence of precomputed coefficients without adding additional operations; increasing efficiency in multiphysics simulations where cross sections can be subject to change. The new formulation is implemented in the MPACT code and tested on two problems: 3D transport assembly calculations using MPACT’s 2D/1D method and a 3D assembly with T/H feedback using MPACT’s 2D/1D method coupled with COBRA-TF. This work demonstrates that the new linear source formulation allows for the number of mesh elements to be significantly reduced while maintaining accuracy, leading to shorter run-times for 3D cases with fixed cross sections, and substantial reduction of memory usage for 3D cases with fixed cross sections. The multiphysics calculations show similar runtimes for the same accuracy with significant reduction of memory. For similar accuracy, the method proved effective in reducingmemory usage by, on average, 30% for 3D problems and 21% for multiphysics problems.

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems

Point-block matrices arise naturally in multiphysics problems when all variables associated with a mesh point are ordered together, and are different from the general block matrices since the sizes of the blocks are so small one can often invert some of the diagonal blocks explicitly. Motivated by the recent works of Chow and Patel and Chow et al., we propose an efficient incomplete LU (ILU) preconditioner for point-block matrices targeting applications on GPU. The construction of the preconditioner involves two critical steps: (1) the initial guessing of values for the lower and upper triangular matrices; and (2) several sweeps of asynchronous updating of the triangular matrices. Three representative problems are studied to show the advantage of the proposed point-block approach over the standard point-wise approach in terms of the number of GMRES iterations and also the total compute time. Moreover, we compare the proposed algorithm with the level-scheduling based parallel algorithm employed in NVIDIA’s cuSPARSE library as well as the serial method implemented in Intel MKL library, and the experiments show that a 2×–5× speedup can be achieved over the block-based ILU( p) factorizations from the cuSPARSE library.

PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts.