We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on an hydrodynamical Drift Flux Model (DFM) combined with a No Pressure Wave approximation of the momentum equation. The focus of this work is on the design of a robust discretization accounting for slanted and multibranch wells with the ability to simulate both transient behavior such as well opening as well as coupled simulations at the time scale of the reservoir. It is based on a staggered finite volume scheme in space combined with a fully implicit Euler time integration. The construction of consistent and stable numerical fluxes is a key feature for a robust numerical method. It is achieved by combining a monotone flux approximation for the phase superficial velocities with an upwind approximation of the phase molar fractions, density and enthalpy. In order to facilitate the coupling of the well and reservoir models, the Newton linearization accounts for the elimination of the hydrodynamical unknowns leading to Jacobian systems using the same primary unknowns than those of the reservoir model. The efficiency of our approach is investigated on both stand alone well test cases without and with cross flow, and on a fully coupled well-reservoir simulation.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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We introduce a fine-grained framework for uncertainty quantification of predictive models under distributional shifts. This framework distinguishes the shift in covariate distributions from that in the conditional relationship between the outcome (Y) and the covariates (X). We propose to reweight the training samples to adjust for an identifiable covariate shift while protecting against worst-case conditional distribution shift bounded in an $f$-divergence ball. Based on ideas from conformal inference and distributionally robust learning, we present an algorithm that outputs (approximately) valid and efficient prediction intervals in the presence of distributional shifts. As a use case, we apply the framework to sensitivity analysis of individual treatment effects with hidden confounding. The proposed methods are evaluated in simulation studies and three real data applications, demonstrating superior robustness and efficiency compared with existing benchmarks.
We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for the Helmholtz equation with rotationally invariant variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus domain) and concentric annuli cells. The discretization preserves the Fourier mode decoupling of rotationally invariant operators, such as the Laplacian, which manifests as block diagonal mass and stiffness matrices. Moreover, the matrices have a sparsity pattern independent of the order of the discretization and admit an optimal complexity factorization. The sparse $hp$-FEM can handle radial discontinuities in the right-hand side and in rotationally invariant Helmholtz coefficients. We consider examples such as a high-frequency Helmholtz equation with radial discontinuities, the time-dependent Schr\"odinger equation, and an extension to a three-dimensional cylinder domain, with a quasi-optimal solve, via the Alternating Direction Implicit (ADI) algorithm.
Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios.
Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the process zone but small compared to that of the application. The specific configuration (both geometrical and mechanical) of this mesoscale heterogeneity is generally recognized as important in determining crack propagation and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic crack propagation is affected by mesoscale heterogeneities taking the form of an array of inclusions. Using a variational phase-field approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation under Mode-I loading across different configurations of these inclusions. If fixing the volume fraction of inclusions, matching the inclusion size to the K-dominance zone size gives rise to the best toughening outcome. Conversely, if varying the volume fraction of inclusions, a lower volume fraction configuration can lead to a better toughening outcome if and only if the inclusion size approaches from above the size of the K-dominance zone. Since the size of the K-dominance zone can be estimated \textit{a priori} given an understanding of the application scenario and material availability, we can, in principle, exploit this estimation to design a material's mesoscale heterogeneity that optimally balances the tradeoff between strength and toughness. This paves the way for realizing functional (meta-)materials against crack propagation in extreme environments.
This paper is concerned with an inverse wave-number-dependent/frequency-dependent source problem for the Helmholtz equation. In d-dimensions (d = 2,3), the unknown source term is supposed to be compactly supported in spatial variables but independent on x_d. The dependance of the source function on k is supposed to be unknown. Based on the Dirichlet-Laplacian method and the Fourier-Transform method, we develop two effcient non-iterative numerical algorithms to recover the wave-number-dependent source. Uniqueness and increasing stability analysis are proved. Numerical experiments are conducted to illustrate the effctiveness and effciency of the proposed method.
Error estimates of cubic interpolated pseudo-particle scheme (CIP scheme) for the one-dimensional advection equation with periodic boundary conditions are presented. The CIP scheme is a semi-Lagrangian method involving the piecewise cubic Hermite interpolation. Although it is numerically known that the space-time accuracy of the scheme is third order, its rigorous proof remains an open problem. In this paper, denoting the spatial and temporal mesh sizes by $ h $ and $ \Delta t $ respectively, we prove an error estimate $ O(\Delta t^3 + \frac{h^4}{\Delta t}) $ in $ L^2 $ norm theoretically, which justifies the above-mentioned prediction if $ h = O(\Delta t) $. The proof is based on properties of the interpolation operator; the most important one is that it behaves as the $ L^2 $ projection for the second-order derivatives. We remark that the same strategy perfectly works as well to address an error estimate for the semi-Lagrangian method with the cubic spline interpolation.
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are mathematically more tractable. However, an integral-equation formulation poses a significant computational challenge: solving large dense linear systems that arise upon discretization. In cases where iterative methods converge rapidly, existing methods that draw on fast summation schemes such as the Fast Multipole Method are highly efficient and well-established. More recently, linear complexity direct solvers that sidestep convergence issues by directly computing an invertible factorization have been developed. However, storage and computation costs are high, which limits their ability to solve large-scale problems in practice. In this work, we introduce a distributed-memory parallel algorithm based on an existing direct solver named ``strong recursive skeletonization factorization.'' Specifically, we apply low-rank compression to certain off-diagonal matrix blocks in a way that minimizes computation and data movement. Compared to iterative algorithms, our method is particularly suitable for problems involving ill-conditioned matrices or multiple right-hand sides. Large-scale numerical experiments are presented to show the performance of our Julia implementation.
We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond 12, which previous methods could not achieve. The new algorithm is applied to the Coxeter-Todd lattice $K_{12}$ as well as to a family of lattices obtained from laminating $K_{12}$. By optimizing this family, we obtain a new best 13-dimensional lattice quantizer (among the lattices with published exact quantizer constants).
Shape memory alloys are remarkable 'smart' materials used in a broad spectrum of applications, ranging from aerospace to robotics, thanks to their unique thermomechanical coupling capabilities. Given the complex properties of shape memory alloys, which are largely influenced by thermal and mechanical loads, as well as their loading history, predicting their behavior can be challenging. Consequently, there exists a pronounced demand for an efficient material model to simulate the behavior of these alloys. This paper introduces a material model rooted in Hamilton's principle. The key advantages of the presented material model encompass a more accurate depiction of the internal variable evolution and heightened robustness. As such, the proposed material model signifies an advancement in the realistic and efficient simulation of shape memory alloys.
We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO$_2$ sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.
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