Numerical Modelling of Convection-Driven Cooling, Deformation and Fracturing of Thermo-Poroelastic Media

Convection-driven cooling in porous media influences thermo-poro-mechanical stresses, thereby causing deformation. These processes are strongly influenced by the presence of fractures, which dominate flow and heat transfer. At the same time, the fractures deform and propagate in response to changes in the stress state. Mathematically, the model governing the physics is tightly coupled and must account for the strong discontinuities introduced by the fractures. Over the last decade, and motivated by a number of porous media applications, research into such coupled models has advanced modelling of processes in porous media substantially. Building on this effort, this work presents a novel model that couples fracture flow and heat transfer and deformation and propagation of fractures with flow, heat transfer and thermo-poroelasticity in the matrix. The model is based on explicit representation of fractures in the porous medium and discretised using multi-point finite volume methods. Frictional contact and non-penetration conditions for the fractures are handled through active set methods, while a propagation criterion based on stress intensity factors governs fracture extension. Considering both forced and natural convection processes, numerical results show the intricate nature of thermo-poromechanical fracture deformation and propagation.

Noncompressed cylindrical layer shock loading in anisothermic conditions

На примере нескольких задач о нагружении упруговязкопластического и термоупругого цилиндрических слоёв с предварительными деформациями показаны основные моменты, на которые следует обратить внимание при комплексном моделировании отклика на существенно нестационарное воздействие термоупругой несжимаемой среды с вязкопластическими свойствами. Отмечены нюансы, касающиеся употребления соотношений теории больших упругопластических деформаций, применения метода лучевых рядов и использования специальных схем численных расчётов. Представлены зависимости скачков температуры и добавочного давления на плоскополяризованных поверхностях сильного разрыва, определены скорости волн нагрузки и круговой поляризации. The main points witch should be paid attention of modeling the response of thermoelastic incompressible medium with viscoplastic properties to the essentially unsteady effect are shown by the example of several problems on loading elastoviscoplastic and thermoelastic cylindrical layers with preliminary deformations. Some remarks were noted regarding to the use of the relations of the theory of finite elastoplastic deformations, the ray series method application and special numerical calculation schemes. The dependencies of temperature and additional pressure breaks on plane-polarized strong discontinuities surfaces, loading and circular polarized waves velocities are determined.

Compatibility of strong discontinuities in micropolar thermoelastic media. A pseudotensor formulation

В статье рассматривается процедура вывода условий совместности на поверхностях сильных разрывов в микрополярных термоупругих средах. Условия совместности сильных разрывов 4-тензора Пиолы-Кирхгофа и 4-тензора энергии-импульса выводятся из принципа наименьшего действия. Приведена определяющая форма микрополярного термоупругого потенциала для изотропных и гемитропных сред. Развиваемая псевдотензорная формулировка условий совместности сильных разрывов может быть применена при моделировании динамики изотропных и гемитропных микрополярных термоупругих сред. The paper deals with the regular procedures for deriving compatibility conditions on the surfaces of strong discontinuities in thermoelastic micropolar media. The jump conditions of the Piola-Kirchhoff 4-pseudotensor and the energy-momentum 4-pseudotensor are derived from the principle of least action. The compatibility conditions on the propagating strong discontinuity surface are explicitly formulated for a micropolar thermoelastic continuum. The developed pseudotensor formulation of the compatibility conditions for strong discontinuities can be applied to the dynamic problems for isotropic and hemitropic micropolar thermoelastic media.

Macrohomogeneity condition for strain gradient homogenization of periodic heterogeneous media with interfacial strong discontinuities

The Hill macrohomogeneity condition is revisited in the context of strain gradient homogenization for heterogeneous materials prone to interfacial displacement jumps. The consideration of strain gradient effects is motivated by their use as a regularization method for strain-softening constitutive damage models leading to strain localization and displacement discontinuity. Starting from the weak form of the boundary value problem formulated at the microscopic level, a polynomial expression of the virtual velocity is adopted as the minimum microscopic kinematics consistent with the selected macroscopic kinematics of the strain gradient effective continuum. The effective volumetric and interfacial mesoscopic strains and stress measures for the effective substitution are obtained versus the microscopic strains and stresses. The Hill macrohomogeneity condition is successively formulated for continuous interfaces and discontinuous interfaces witnessing strong discontinuities. It highlights the expressions of the effective stress measures associated to the volumetric and interfacial behavior for both classical and higher-order effects.

Enhanced numerical integration scheme based on image compression techniques: Application to rational polygonal interpolants

Polygonal finite elements offer an increased freedom in terms of mesh generation at the price of more complex, often rational, shape functions. Thus, the numerical integration of rational interpolants over polygonal domains is one of the challenges that needs to be solved. If, additionally, strong discontinuities are present in the integrand, e.g., when employing fictitious domain methods, special integration procedures must be developed. Therefore, we propose to extend the conventional quadtree-decomposition-based integration approach by image compression techniques. In this context, our focus is on unfitted polygonal elements using Wachspress shape functions. In order to assess the performance of the novel integration scheme, we investigate the integration error and the compression rate being related to the reduction in integration points. To this end, the area and the stiffness matrix of a single element are computed using different formulations of the shape functions, i.e., global and local, and partitioning schemes. Finally, the performance of the proposed integration scheme is evaluated by investigating two problems of linear elasticity.

Smoothed particle magnetohydrodynamics with the geometric density average force expression

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme (SPMHD) using the geometric density average force expression. Geometric density average within smoothed particle hydrodynamics (GDSPH) has recently been shown to reduce the leading order errors and greatly improve the accuracy near density discontinuities, eliminating surface tension effects. Here, we extend the study to investigate how SPMHD benefits from this method. We implement ideal MHD in the GASOLINE2 and CHANGA codes with both GDSPH and traditional smoothed particle hydrodynamics (TSPH) schemes. A constrained hyperbolic divergence cleaning scheme was employed to control the divergence error and a switch for artificial resistivity with minimized dissipation was also used. We tested the codes with a large suite of MHD tests and showed that in all problems, the results are comparable or improved over previous SPMHD implementations. While both GDSPH and TSPH perform well with relatively smooth or highly supersonic flows, GDSPH shows significant improvements in the presence of strong discontinuities and large dynamic scales. In particular, when applied to the astrophysical problem of the collapse of a magnetized cloud, GDSPH realistically captures the development of a magnetic tower and jet launching in the weak-field regime, while exhibiting fast convergence with resolution, whereas TSPH failed to do so. Our new method shows qualitatively similar results to those of the meshless finite mass/volume schemes within the GIZMO code, while remaining computationally less expensive.