Multi-task unscented Kalman inversion (MUKI): a derivative-free joint inversion framework and its application to joint inversion of geophysical data

In the geophysical joint inversion, the gradient and Bayesian Markov Chain Monte Carlo (MCMC) sampling-based methods are widely used owing to their fast convergences or global optimality. However, these methods either require the computation of gradients and easily fall into local optimal solutions, or cost much time to carry out the millions of forward calculations in a huge sampling space. Different from these two methods, taking advantage of the recently developed unscented Kalman method in computational mathematics, we extend an iterative gradient-free Bayesian joint inversion framework, i.e., Multi-task unscented Kalman inversion (MUKI). In this new framework, information from various observations is incorporated, the model is iteratively updated in a derivative-free way, and a Gaussian approximation to the posterior distribution of the model parameters is obtained. We apply the MUKI to the joint inversion of receiver functions and surface wave dispersion, which is well-established and widely used to construct the crustal and upper mantle structure of the earth. Based on synthesized and real data, the tests demonstrate that MUKI can recover the model more efficiently than the gradient-based method and the Markov Chain Monte Carlo method, and it would be a promising approach to resolve the geophysical joint inversion problems.Comment: 13 pages, 4 figure

Phase-field-lattice Boltzmann method for dendritic growth with melt flow and thermosolutal convection–diffusion

We propose a new phase-field model formulated within the system of lattice Boltzmann (LB) equation for simulating solidification and dendritic growth with fully coupled melt flow and thermosolutal convection–diffusion. With the evolution of the phase field and the transport phenomena all modeled and integrated within the same LB framework, this method preserves and combines the intrinsic advantages of the phase-field method (PFM) and the lattice Boltzmann method (LBM). Particularly, the present PFM/LBM model has several improved features compared to the existing phase-field models including: (1) a novel multiple-relaxation-time (MRT) LB scheme for the phase-field evolution is proposed to effectively model solidification coupled with melt flow and thermosolutal convection–diffusion with improved numerical stability and accuracy, (2) convenient diffuse interface treatments are implemented for the melt flow and thermosolutal transport which can be applied to the entire domain without tracking the interface, and (3) the evolution of the phase field, flow, concentration, and temperature fields on the level of microscopic distribution functions in the LB schemes is decoupled with a multiple-time-scaling strategy (despite their full physical coupling), thus solidification at high Lewis numbers (ratios of the liquid thermal to solutal diffusivities) can be conveniently modeled. The applicability and accuracy of the present PFM/LBM model are verified with four numerical tests including isothermal, iso-solutal and thermosolutal convection–diffusion problems, where excellent agreement in terms of phase-field and thermosolutal distributions and dendritic tip growth velocity and radius with those reported in the literature is demonstrated. The proposed PFM/LBM model can be an attractive and powerful tool for large-scale dendritic growth simulations given the high scalability of the LBM

Lattice Boltzmann-based Sharp-interface schemes for conjugate heat and mass transfer and diffuse-interface schemes for Dendritic growth modeling

Analyses of heat and mass transfer between different materials and phases are essential in numerous fundamental scientific problems and practical engineering applications, such as thermal and chemical transport in porous media, design of heat exchangers, dendritic growth during solidification, and thermal/mechanical analysis of additive manufacturing processes. In the numerical simulation, interface treatment can be further divided into sharp interface schemes and diffuse interface schemes according to the morphological features of the interface. This work focuses on the following subjects through computational studies: (1) critical evaluation of the various sharp interface schemes in the literature for conjugate heat and mass transfer modeling with the lattice Boltzmann method (LBM), (2) development of a novel sharp interface scheme in the LBM for conjugate heat and mass transfer between materials/phases with very high transport property ratios, and (3) development of a new diffuse-interface phase-field-lattice Boltzmann method (PFM/LBM) for dendritic growth and solidification modeling. For comparison of the previous sharp interface schemes in the LBM, the numerical accuracy and convergence orders are scrutinized with representative test cases involving both straight and curved geometries. The proposed novel sharp interface scheme in the LBM is validated with both published results in the literature as well as in-house experimental measurements for the effective thermal conductivity (ETC) of porous lattice structures. Furthermore, analytical correlations for the normalized ETC are proposed for various material pairs and over the entire range of porosity based on the detailed LBM simulations. In addition, we provide a modified correlation based on the SS420-air and SS316L-air metal pairs and the high porosity range for specific application. The present PFM/LBM model has several improved features compared to those in the literature and is capable of modeling dendritic growth with fully coupled melt flow and thermosolutal convection-diffusion. The applicability and accuracy of the PFM/LBM model is verified with numerical tests including isothermal, iso-solutal and thermosolutal convection-diffusion problems in both 2D and 3D. Furthermore, the effects of natural convection on the growth of multiple crystals are numerically investigated

Effect of Nano-clay on Rheological and Extrusion Foaming Process of a Block-Copolymerized Polypropylene

The effects of nano-clay and the corresponding coupling agent maleic anhydride grafted polypropylene (PP-g-MAH) on thermal properties, rheological properties and extrusion foaming process of a block-copolymerized polypropylene (B-PP) were studied. Supercritical CO2 (SC CO2) was used as the foaming agent with a concentration of 5wt%. Each step of foamed B-PP/ PP-g-MAH/ nano-clay composites processing is addressed, including mixing of the composites, manufacture of the composites, foaming process of the composites and characterization of the cell structure. The results showed that incorporation of nano-clay and PP-g-MAH caused reduced melt strength and complex viscosity of B-PP. However, the heterogeneous nucleation induced by nano-clay and PP-g-MAH improved the maximum foaming expansion ratio and cell-population density of B-PP foam

Effect of Nano-clay on Rheological and Extrusion Foaming Process of a Block-Copolymerized Polypropylene

The effects of nano-clay and the corresponding coupling agent maleic anhydride grafted polypropylene (PP-g-MAH) on thermal properties, rheological properties and extrusion foaming process of a block-copolymerized polypropylene (B-PP) were studied. Supercritical CO2 (SC CO2) was used as the foaming agent with a concentration of 5wt%. Each step of foamed B-PP/ PP-g-MAH/ nano-clay composites processing is addressed, including mixing of the composites, manufacture of the composites, foaming process of the composites and characterization of the cell structure. The results showed that incorporation of nano-clay and PP-g-MAH caused reduced melt strength and complex viscosity of B-PP. However, the heterogeneous nucleation induced by nano-clay and PP-g-MAH improved the maximum foaming expansion ratio and cell-population density of B-PP foam

Multi-task Unscented Kalman Inversion for joint inversion of receiver function and surface wave dispersion

Based on the recently developed theory of Unscented Kalman Inversion in computational mathematics, we proposed a Bayesian joint inversion framework, i.e., Multi-task Unscented Kalman Inversion (MTUKI), and apply it to the joint inversion of receiver function (RF) and surface wave dispersion (SWD). This method can share information between different observations in a derivative-free way and provide an efficient Gaussian approximation to the posterior distribution of model parameters (thickness and S-wave velocity in each layer of media). The theory and experiments show that our proposed framework demonstrates superior performance in terms of robustness, accuracy, and high efficiency.Comment: 5 pages, 3 figure