Scaling carbon sequestration phenomena to the earth's surface

We present a computational framework for fast monitoring of fault stability and ground deformation in multiphase geomechanics and demonstrate its efficacy for a carbon sequestration--enhanced oil recovery case study. The staggered solution algorithm for the coupled problem is augmented with a feature that allows for the flow and geomechanics sub-problems to be solved on different unstructured tetrahedral grids. For the field scale problem, the geomechanics grid goes all the way to the free surface while the flow grid is truncated at a depth above which the layers are impermeable. This framework avoids the unnecessary computational burden associated with equilibrating the initial pressure solution in the overburden, allows for a study of the critical interaction between overburden and faults, allows for fast renditions of ground deformation, and allows a choice of resolution for the flow and geomechanics grids independently to capture disparate length scales of the underlying physics.

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.

Numerical Algorithms for Simulation of a Fluid-Filed Fracture Evolution in a Poroelastic Medium

The paper deals with the computational framework for the numerical simulation of the three dimensional fluid-filled fracture evolution in a poroelastic medium. The model consists of several groups of equations including the Biot poroelastic model to describe a bulk medium behavior, Reynold’s lubrication equations to describe a flow inside fracture and corresponding bulk/fracture interface conditions. The geometric model of the fracture assumes that it is described as an arbitrary sufficiently smooth surface with a boundary. Main attention is paid to describing numerical algorithms for particular problems (poroelasticity, fracture fluid flow, fracture evolution) as well as an algorithm for the coupled problem solution. An implicit fracture mid-surface representation approach based on the closest point projection operator is a particular feature of the proposed algorithms. Such a representation is used to describe the fracture mid-surface in the poroelastic solver, Reynold’s lubrication equation solver and for simulation of fracture evolutions. The poroelastic solver is based on a special variant of X-FEM algorithms, which uses the closest point representation of the fracture. To solve Reynold’s lubrication equations, which model the fluid flow in fracture, a finite element version of the closet point projection method for PDEs surface is used. As a result, the algorithm for the coupled problem is purely Eulerian and uses the same finite element mesh to solve equations defined in the bulk and on the fracture mid-surface. Finally, we present results of the numerical simulations which demonstrate possibilities of the proposed numerical techniques, in particular, a problem in a media with a heterogeneous distribution of transport, elastic and toughness properties.

Error Estimation of Euler Method for the Instationary Stokes–Biot Coupled Problem

In this paper, we study a finite element computational model for solving the interaction between a fluid and a poroelastic structure that couples the Stokes equations with the Biot system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is used to impose weakly this condition. With the obtained finite element solutions, the error estimators are performed for the fully discrete formulations.

QoS-Aware Power Allocation for Multi-UAV Aided Networks

UAV base stations (UAVBS’s) have been proposed as a revolution for the new architecture of 5G networks. The UAVBS’s can be deployed as access points to provide wireless services to users in emergency scenarios. However, it is challenging to solve the highly coupled problem for UAVBS deployment and power allocation. In the meanwhile, the hybrid analog and digital beamforming is leverage to reduce the hardware cost for beamforming in 5G networks. In this work, we first use k-means algorithm to solve the 3D placement of UAVBS’s by exploiting the optimal coverage altitude. Next, power allocation problem is resolved using the difference-of-two-convex functions (D.C.) programming algorithm. Furthermore, the quality of service (QoS) for each user is guaranteed by adjusting the transmitted power. Finally, extensive experiments are conducted to demonstrate the feasibility of the proposed algorithm.

Inexact Methods for Black-Oil Sequential Fully Implicit SFI Scheme

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually fully solved at each outer iteration. This can result in wasted computations that contribute little towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost while maintain or improve the convergence of SFI by preventing ‘over-solving’. We first developed a framework based on the nonlinear acceleration techniques (Jiang and Tchelepi 2019) to ensure robust outer-loop convergence. We then developed inexact-type methods that prevent ‘over-solving’ and minimize the cost of inner solvers for SFI. The motivation is similar to the inexact Newton method, where the inner (linear) iterations are controlled in a way that the outer (Newton) convergence is not degraded, but the overall computational effort is greatly reduced. We proposed an adaptive strategy that provides relative tolerances based on the convergence rates of the coupled problem. The developed inexact SFI method was tested using numerous simulation studies. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers. The test cases included synthetic as well as real-field models with complex flow physics and high heterogeneity. The results show that the basic SFI method is quite inefficient. When the coupling is strong, we observed that the outer convergence is mainly restricted by the initial residuals of the sub-problems. It was observed that the feedback from one inner solver can cause the residual of the other to rebound to a much higher level. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall residual. By comparison, the inexact SFI method adaptively provided the relative tolerances adequate for the sub-problems. We show across a wide range of flow conditions that the inexact SFI can effectively resolve the ‘over-solving’ issue, and thus greatly improve the overall performance. The novel information of this paper includes: 1) we found that for SFI, there is no need for one sub-problem to strive for perfection (‘over-solving’), while the coupled residual remains high because of the other sub-problem; 2) a novel inexact SFI method was developed to prevent ‘over-solving’ and minimize the cost of inner solvers; 3) an adaptive strategy was proposed for relative tolerances based on the convergence rates of the coupled problem; and 4) a novel SFI framework was developed based on the nonlinear acceleration techniques to ensure robust outer-loop convergence.

A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

Motivated by the influence of deformation-induced microcracks on the effective electrical properties at the macroscale, an electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed. The formulation accounts for finite deformation processes and is a direct extension of the fundamental theoretical developments presented by Kaiser and Menzel (Arch Appl Mech 91:1509–1526, 2021) who assume a geometrically linearised setting. More specifically speaking, averaging theorems for the electric field quantities are proposed and boundary conditions that a priori fulfil the extended Hill–Mandel condition of the electro-mechanically coupled problem are discussed. A study of representative boundary value problems in two- and three-dimensional settings eventually shows the applicability of the proposed formulation and reveals the severe influence of microscale deformation processes on the effective electrical properties at the macroscale.

Frequency and Amplitude Modulations of a Moving Structure in Unsteady Non-Homogeneous Density Fluid Flow

A fluid-structure interaction’s effects on the dynamics of a hydrofoil immersed in a fluid flow of non-homogeneous density is presented and analyzed. A linearized model is applied to solve the fluid-structure coupled problem. Fluid density variations along the hydrofoil upper surface, based on the sinusoidal cavity oscillations, are used. It is shown that for the steady cavity case, the value of cavity length Lp does not affect the amplitude of the hydrofoil displacements. However, the natural frequency of the structure increases according to Lp. In the unsteady cavity case, the variations of the added mass and added damping (induced by the fluid density rate of change) generate frequency and amplitude modulations in the hydrofoil dynamics. To analyse this phenomena, the empirical mode decomposition, a well established data-driven method to handle such modulations, is used.