Numerical Convection Models Research Articles

A basal magma ocean dynamo to explain the early lunar magnetic field

The source of the ancient lunar magnetic field is an unsolved problem in the Moon's evolution. Theoretical work invoking a core dynamo has been unable to explain the magnitude of the observed field, falling instead one to two orders of magnitude below it. Since surface magnetic field strength is highly sensitive to the depth and size of the dynamo region, we instead hypothesize that the early lunar dynamo was driven by convection in a basal magma ocean formed from the final stages of an early lunar magma ocean; this material is expected to be dense, radioactive, and metalliferous. Here we use numerical convection models to predict the longevity and heat flow of such a basal magma ocean and use scaling laws to estimate the resulting magnetic field strength. We show that, if sufficiently electrically conducting, a magma ocean could have produced an early dynamo with surface fields consistent with the paleomagnetic observations.

Numerical modelling of natural convection in a square cavity: effect of nanofluid volume fraction and inclination

In this paper, the phenomenon of natural convection in a square cavity filled with copper (Cu) -based nanofluid (Nf) has been studied. The influences of the volume fraction (ф) on the convective flow, as well as the effect of the inclination (γ) of the cavity on thermal performances were examined. The dimensionless governing equations formulated using stream function, vorticity, and temperatures were solved by finite difference methods, where the Successive Over-Relaxation (SOR) iteration and the upwind scheme were adopted. The developed code served as a verification of results where it showed a good agreement with previous works. The calculation code was then used to visualize the influence of the inclination on the thermal enhancement and showed that the transfer becomes more efficient with an inclination of π/6.

Inverse Problems in Geodynamics Using Machine Learning Algorithms

AbstractDuring the past few decades numerical studies have been widely employed to explore the style of circulation and mixing in the mantle of Earth and other planets. However, in geodynamical studies there are many properties from mineral physics, geochemistry, and petrology in these numerical models. Machine learning, as a computational statistic‐related technique and a subfield of artificial intelligence, has rapidly emerged recently in many fields of sciences and engineering. We focus here on the application of supervised machine learning (SML) algorithms in predictions of mantle flow processes. Specifically, we emphasize on estimating mantle properties by employing machine learning techniques in solving an inverse problem. Using snapshots of numerical convection models as training samples, we enable machine learning models to determine the magnitude of the spin transition‐induced density anomalies that can cause flow stagnation at midmantle depths. Employing support vector machine algorithms, we show that SML techniques can successfully predict the magnitude of mantle density anomalies and can also be used in characterizing mantle flow patterns. The technique can be extended to more complex geodynamic problems in mantle dynamics by employing deep learning algorithms for putting constraints on properties such as viscosity, elastic parameters, and the nature of thermal and chemical anomalies.

Aspects of numerical modeling of mixed convection over heated horizontal plate

Mixed convection is a common type of heat transfer for relatively slow impinging flows. When fluid flow impinges a transverse flat plate a Hiemenz flow appears. It is basically driven by buoyancy forces, which make it unstable and challenging to simulate. The present study is dedicated to these challenges in terms of computational mesh reduction. Several methods of mesh reduction were tested, including computational domain simplification, symmetry application and mesh coarsening. Each simplification method was tested against experimental data to evaluate proposed hypotheses about symmetry applicability and unconditional advantage of finer meshes. All considered cases were simulated with previously validated numerical model. Although simulated process was seemingly purely symmetrical, it didn’t respond well to implementation of symmetrical boundary conditions. Simplification of computational domain yielded generally expected results showing significant deterioration after truncation of essential part of domain. Mesh coarsening led to erroneous results as well, but dependency wasn’t linear. Statistical analysis proved normality of simulation errors distribution. The present study addresses preprocessing stage of simulation process, providing some insight into simplification methods of computational mesh.

The Magnitude of Viscous Dissipation in Strongly Stratified Two-dimensional Convection

Abstract Convection in astrophysical systems must be maintained against dissipation. Although the effects of dissipation are often assumed to be negligible, theory suggests that in strongly stratified convecting fluids, the dissipative heating rate can exceed the luminosity carried by convection. Here, we explore this possibility using a series of numerical simulations. We consider two-dimensional numerical models of hydrodynamic convection in a Cartesian layer under the anelastic approximation and demonstrate that the dissipative heating rate can indeed exceed the imposed luminosity. We establish a theoretical expression for the ratio of the dissipative heating rate to the luminosity emerging at the upper boundary, in terms only of the depth of the layer and the thermal scale height. In particular, we show that this ratio is independent of the diffusivities and confirm this with a series of numerical simulations. Our results suggest that dissipative heating may significantly alter the internal dynamics of stars and planets.

Numerical simulation of fluid flow and heat transfer in rotating channels using parallel lattice Boltzmann method

This paper presents a numerical modeling and simulation of incompressible laminar mixed convection in rotating channels using parallel lattice Boltzmann method. Individual distribution functions with D3Q19 and D3Q6 lattice types were considered to solve fluid flow and heat transfer problems, respectively. The Reynolds number was set to 100, and wall-to-inlet fluid density ratio was set to 0.2. Two rotation modes namely orthogonal and parallel modes were considered with rotation number equal to 0.2. LBM code was written in C language and was parallelized using OpenMP libraries. Domain decomposition method of data parallelism was adopted here, and simulations were conducted on a workstation with dual processors and 64GB RAM. Predicted velocity and temperature fields were found to agree well with velocity and temperature obtained from Fluent.

ADOPT: A tool for automatic detection of tectonic plates at the surface of convection models

AbstractMantle convection models with plate‐like behavior produce surface structures comparable to Earth's plate boundaries. However, analyzing those structures is a difficult task, since convection models produce, as on Earth, diffuse deformation and elusive plate boundaries. Therefore we present here and share a quantitative tool to identify plate boundaries and produce plate polygon layouts from results of numerical models of convection: Automatic Detection Of Plate Tectonics (ADOPT). This digital tool operates within the free open‐source visualization software Paraview. It is based on image segmentation techniques to detect objects. The fundamental algorithm used in ADOPT is the watershed transform. We transform the output of convection models into a topographic map, the crest lines being the regions of deformation (plate boundaries) and the catchment basins being the plate interiors. We propose two generic protocols (the field and the distance methods) that we test against an independent visual detection of plate polygons. We show that ADOPT is effective to identify the smaller plates and to close plate polygons in areas where boundaries are diffuse or elusive. ADOPT allows the export of plate polygons in the standard OGR‐GMT format for visualization, modification, and analysis under generic softwares like GMT or GPlates.

Experiments Using a Ground-Based Electrostatic Levitator and Numerical Modeling of Melt Convection for the Iron-Cobalt System in Support of Space Experiments

Materials research is being conducted using an electromagnetic levitator installed in the International Space Station. Various metallic alloys were tested to elucidate unknown links among the structures, processes, and properties. To accomplish the mission of these space experiments, several ground-based activities have been carried out. This paper presents some of our ground-based supporting experiments and numerical modeling efforts. Mass evaporation of Fe50Co50, one of the flight compositions, was predicted numerically and validated by the tests using an electrostatic levitator (ESL). The density of various compositions within the Fe-Co system was measured with ESL. These results serve as reference data for the space experiments. The convection inside a electromagnetically-levitated droplet was also modeled to predict the flow status, shear rate, and convection velocity under various process parameters, which is essential information for designing and analyzing the space experiments of some flight compositions influenced by convection.

Continental crust formation on early Earth controlled by intrusive magmatism.

The global geodynamic regime of early Earth, which operated before the onset of plate tectonics, remains contentious. As geological and geochemical data suggest hotter Archean mantle temperature and more intense juvenile magmatism than in the present-day Earth, two crust-mantle interaction modes differing in melt eruption efficiency have been proposed: the Io-like heat-pipe tectonics regime dominated by volcanism and the "Plutonic squishy lid" tectonics regime governed by intrusive magmatism, which is thought to apply to the dynamics of Venus. Both tectonics regimes are capable of producing primordial tonalite-trondhjemite-granodiorite (TTG) continental crust but lithospheric geotherms and crust production rates as well as proportions of various TTG compositions differ greatly, which implies that the heat-pipe and Plutonic squishy lid hypotheses can be tested using natural data. Here we investigate the creation of primordial TTG-like continental crust using self-consistent numerical models of global thermochemical convection associated with magmatic processes. We show that the volcanism-dominated heat-pipe tectonics model results in cold crustal geotherms and is not able to produce Earth-like primordial continental crust. In contrast, the Plutonic squishy lid tectonics regime dominated by intrusive magmatism results in hotter crustal geotherms and is capable of reproducing the observed proportions of various TTG rocks. Using a systematic parameter study, we show that the typical modern eruption efficiency of less than 40 per cent leads to the production of the expected amounts of the three main primordial crustal compositions previously reported from field data (low-, medium- and high-pressure TTG). Our study thus suggests that the pre-plate-tectonics Archean Earth operated globally in the Plutonic squishy lid regime rather than in an Io-like heat-pipe regime.

Extremely long transition phase of thermal convection in the mantle of massive super-Earths

Adiabatic compression is a key factor that exerts control over thermal convection in the compressible solid mantle of super-Earths. To discuss the effects of adiabatic compression, we present a numerical model of transient convection in the cooling mantle of a super-Earth that is ten times larger in size than the Earth. The calculations started with the shallow mantle that was hotter than expected by the extrapolation from the deep mantle conditions. This type of initial thermal state of the mantle is expected to naturally occur in real super-Earths due to heating by giant impacts at the time of their formation. With our initial setup conditions, the convection temporarily occurs as a layered convection for the first several to ten billion years of the calculation and then changes its style into a whole layer convection. The long duration of the transient stage suggests that mantle convection currently occurs as a temporal layered convection in many of the super-Earths. A temporal layered convection, if it occurs, can exert control over the tectonic activities of super-Earths. Future studies should clarify how internal heating and complicated rheological properties of mantle materials including their pressure dependence affect the duration of the temporal layered convection.Graphical abstract.

Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force

Influence of external magnetic source on Fe3O4-water heat transfer in a cavity with circular hot cylinder is studied. New numerical method is chosen namely CVFEM. Influences of Rayleigh, Hartmann numbers and volume fraction of Fe3O4 on hydrothermal characteristics are presented. Results illustrate that Lorentz forces cause the nanofluid velocity to reduce and augment the thermal boundary layer thickness. The heat transfer improvement enhances with augment of Lorentz forces. Nusselt number augments with rise of buoyancy forces but it reduces with augment of Lorentz forces.

Effect of Convective Transport in Porous Media on the Conditions of Organic Matter Maturation and Generation of Hydrocarbons in Trap Rocks Complexes

By analyze of catalysis processes of hydrocarbons and oil in the medium with the oil source rocks usually it is used the approximation about homogeneous medium and homogeneous РТ- conditions in it. But the oil source rocks are porous medium, the slow flows in which are influenced by convection, which leads to significant heterogeneities of the structure of РТ- conditions of oil source matter ripening. These structures can be either stationary or no stationary. In that paper we developed results of numerical modeling of convection in homogeneous medium and in the medium that contains heterogeneous for permeability 2D and 3D inclusions for detection and quantitative estimation the convection influence on the volume oil source rocks estimation in which the oil catalysis conditions are realized. It is showed that the amount of oil forming significantly depends from the convection intensity.

Viscosity distribution in the mantle convection models

Viscosity is a fundamental property of the mantle which determines the global geodynamical processes. According to the microscopic theory of defects and laboratory experiments, viscosity exponentially depends on temperature and pressure, with activation energy and activation volume being the parameters. The existing laboratory measurements are conducted with much higher strain rates than in the mantle and have significant uncertainty. The data on postglacial rebound only allow the depth distributions of viscosity to be reconstructed. Therefore, spatial distributions (along the depth and lateral) are as of now determined from the models of mantle convection which are calculated by the numerical solution of the convection equations, together with the viscosity dependences on pressure and temperature (PT-dependences). The PT-dependences of viscosity which are presently used in the numerical modeling of convection give a large scatter in the estimates for the lower mantle, which reaches several orders of magnitude. In this paper, it is shown that it is possible to achieve agreement between the calculated depth distributions of viscosity throughout the entire mantle and the postglacial rebound data. For this purpose, the values of the volume and energy of activation for the upper mantle can be taken from the laboratory experiments, and for the lower mantle, the activation volume should be reduced twice at the 660-km phase transition boundary. Next, the reduction in viscosity by an order of magnitude revealed at the depths below 2000 km by the postglacial rebound data can be accounted for by the presence of heavy hot material at the mantle bottom in the LLSVP zones. The models of viscosity spatial distribution throughout the entire mantle with the lithospheric plates are presented.

Numerical modelling of thermal convection in the Luttelgeest carbonate platform, the Netherlands

The presence of convective fluid flow in permeable layers can create zones of anomalously high temperature which can be exploited for geothermal energy. Temperature measurements from the Luttelgeest-01 (LTG-01) well in the northern onshore region of the Netherlands indicate variations in the thermal regime that could be indicative of convection. This thermal anomaly coincides with a 800m interval of Dinantian carbonates showing signs of increased fracture permeability of 6 10−14m2.In this study, we reproduce the thermal gradient at LTG-01 using 3D numerical models in order to better understand the interplay between natural fracture permeability and temperature patterns. Numerical models of thermal convection are used to illustrate the role of permeability on the timing of convection onset, convection structure development and resulting temperature patterns.Rayleigh number calculations indicate that convective flow is realistic within the Luttelgeest carbonate platform. The degree and pattern of convection depends strongly on the platform geometry and thickness, permeability structure and geothermal gradient of the convective zone. The spacing of convective upwellings and their thermal anomalies can be well predicted by numerical models that provide evidence for significant convection-driven thermal anomalies. Numerical models can facilitate in exploration workflows to assess thermal variation and location of upwelling zones.

A rapid burst in hotspot motion through the interaction of tectonics and deep mantle flow.

Volcanic hotspot tracks featuring linear progressions in the age of volcanism are typical surface expressions of plate tectonic movement on top of narrow plumes of hot material within Earth's mantle. Seismic imaging reveals that these plumes can be of deep origin--probably rooted on thermochemical structures in the lower mantle. Although palaeomagnetic and radiometric age data suggest that mantle flow can advect plume conduits laterally, the flow dynamics underlying the formation of the sharp bend occurring only in the Hawaiian-Emperor hotspot track in the Pacific Ocean remains enigmatic. Here we present palaeogeographically constrained numerical models of thermochemical convection and demonstrate that flow in the deep lower mantle under the north Pacific was anomalously vigorous between 100 million years ago and 50 million years ago as a consequence of long-lasting subduction systems, unlike those in the south Pacific. These models show a sharp bend in the Hawaiian-Emperor hotspot track arising from the interplay of plume tilt and the lateral advection of plume sources. The different trajectories of the Hawaiian and Louisville hotspot tracks arise from asymmetric deformation of thermochemical structures under the Pacific between 100 million years ago and 50 million years ago. This asymmetric deformation waned just before the Hawaiian-Emperor bend developed, owing to flow in the deepest lower mantle associated with slab descent in the north and south Pacific.

Three-dimensional numerical modeling of free convection in sloping porous enclosures

Three-dimensional (3D) numerical simulations are carried out to study steady state free convection in a sloping porous enclosure heated from below. The model is based on Darcy’s law and the Boussinesq approximation. Two different approaches to solve this problem are compared: primitive variables and vector potential. Although both numerical models lead to equivalent results in terms of the Nusselt number and convective modes, the vector potential model proved to be less mesh-dependent and also a faster algorithm. A parametric study of the problem considering Rayleigh number, slope angle and aspect ratio showed that convective modes with irregular 3D geometries can develop in a wide variety of situations, including horizontal porous enclosure at relatively low Rayleigh numbers. The convective modes that have been described in previous 2D studies (multicellular and single cell) are also present in the 3D case. Nonetheless the results presented here show that the transition between these convective modes follows an irregular 3D geometry characterized by the interaction of transverse and longitudinal coils.

Stationary fluid convection modes with a Gaussian viscosity dependence of temterature

The results of a numerical modeling of thermo-gravitational convection of abnormally thermo-viscous fluid in a closed square cavity with two vertical adiabatic walls and two horizontal isothermal walls are presented. A model Newtonian liquid for which the dependence of viscosity on temperature is described by a bell function (Gaussian curve) is considered. The natural convection of inhomogeneous liquid is described by the closed mathematical model based on the continuous mechanics equations written in Oberbeck-Boussinesq approximation, where the fluid density is a linear function of temperature. To simulate the fluid flow dynamics, the modified computer code based on the implicit finite volume method and SIMPLE-type algorithm with the second-order temporal accuracy is realized using multiprocessor technology. The effect of the viscosity abnormality on stationary modes of convective flows are studied, the integral heat transfer coefficients in a flat cell are calculated.

Numerical Modeling of Conjugate Thermogravitational Convection in a Closed System with a Radiant Energy Source in Conditions of Convective-Radiative Heat Exchange at the External Boundary

Mathematical modeling of conjugate natural convection in a closed rectangular cavity with a radiant energy source in conditions of convective-radiative heat exchange at the external boundary was conducted. The radiant energy distribution was set by the Lambert’s law. Conduction and convection processes analysis showed that the air masses flow pattern is modified slightly over the time. The temperature increases in the gas cavity, despite the heat removal from the one of the external boundary. According to the results of the integral heat transfer analysis were established that the average Nusselt number (Nuav ) increasing occurs up to τ = 200 (dimensionless time). Further Nuav has changed insignificantly due to the temperature field equalization near the interfaces “gas – wall”.

Influence of continents and lithospheric plates on the shape of {\itshape D$''$}~layer~and~the~spatial~distribution of mantle plumes

The regularities of the global intraplate volcanism of the Earth are explained by the mantle plumes originating at the heads and margins of two piles of dense material of the hot and relatively heavy �� ′′ layer at the base of the mantle. Due to thermal blanket effect under a supercontinent the overheated region with ascending flows arises in the mantle. These flows distort the �� ′′ layer and produce the thermochemical piles in the lowermost mantle under the supercontinent. It is supposed that the pile under Africa originated at the time of existence of Pangea, while the pile under the Pacific Ocean originated at the time of existence of Rodinia. As Africa succeeds to Pangea, the pile under Africa exists until now. But it stays unclear why the pile under the Pacific Ocean exists up to now despite supercontinent Rodinia has been broken-up a long time ago. The numerical models of thermochemical convection in the whole mantle with spherical geometry which include the heavy �� ′′ layer allow to clear up effects of supercontinents and lithospheric plates on deformations of the �� ′′ layer by mantle flows and formation of the thermochemical piles.

A method for numerical modelling of convection–reaction–diffusion using electrical analogues

AbstractIn this paper, a new method, called the lumped‐component circuit method (LCM), is developed for one‐dimensioal and two‐dimensional convection–reaction–diffusion with low to moderate Peclet numbers, tested for modelling both steady‐state and transient problems, and compared with standard finite volume method (FVM) schemes. The method has been developed principally for solving equations with piecewise‐constant coefficients using nodes that are not positioned to correspond to the coefficient discontinuities. In such situations, the FVM solutions do not converge consistently as the node spacing is decreased, but LCM solutions do. In general, the LCM method is more accurate than the FVM schemes tested, and, while the computational cost of LCM is higher, results suggest that it can be more efficient. Like the transmission line method (TLM), it is an indirect scheme in which the problem to be solved is first represented by an analogous transmission line (TL). Unlike with TLM, however, the TL is then modelled using a lumped‐component circuit, the voltages at nodes within that circuit being calculated. Copyright © 2015 John Wiley & Sons, Ltd.