The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if t...
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The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.
Droplet coalescence is a multiscale phenomenon driven by multiple thermodynamic non-equilibrium (TNE) effects. This study investigates the droplet coalescence mechanisms and the interplay between various TNE effects u...
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Droplet coalescence is a multiscale phenomenon driven by multiple thermodynamic non-equilibrium (TNE) effects. This study investigates the droplet coalescence mechanisms and the interplay between various TNE effects under isothermal and non-isothermal conditions kinetically. The main findings include: (1) Coalescence initiation and cut-through mechanisms: In non-isothermal conditions, the temperature rise caused by the release of latent heat during phase transition slightly increases the surface tension gradient (driving force) near the contact point of the two droplets, while significantly enhancing the pressure gradient (resistance). This results in a significantly prolonged coalescence initiation time compared to the isothermal case. The additional temperature field effect increases the spatial complexity of both the flow field and droplet morphology. Regarding the cut-through mechanism, in both cases, pressure extends the liquid-vapor interface in opposite directions, promoting the growth of the liquid bridge. (2) TNE effects: Latent heat-induced temperature rise significantly refrains the TNE intensity in thermal case. Before and after droplet contact, non-equilibrium quantities driven by the temperature gradient (∆∗3,1 and ∆∗3) and those driven by the velocity gradient (∆∗2 and ∆∗4,2), alternate in dominating the coalescence process. This competition and interplay result in a more complex spatial and spatiotemporal evolution of TNE effects compared to the isothermal case, where the TNE intensity is primarily dominated by ∆∗2 and ∆∗4,2. (3) Entropy production mechanisms: In the non-isothermal case, entropy production is contributed not only by ∆∗2 but also by ∆∗3,1, with the former being the dominant contributor. The temperature field reduces the entropy production rate, while extends its duration, and increases the total entropy production. Before and after droplet cut-through, the entropy production rates from ∆∗2 and ∆∗3,1 alternate in dominating the total e
The physical fields in porous materials under strong shock wave reaction are very complicated. We simulate such systems using the grain contact material point method. The complex temperature fields in the material are...
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The physical fields in porous materials under strong shock wave reaction are very complicated. We simulate such systems using the grain contact material point method. The complex temperature fields in the material are treated with the morphological characterization. To compare the structures and evolution of characteristic regimes under various temperature thresholds, we introduce two concepts, structure similarity and process similarity. It is found that the temperature pattern dynamics may show high similarity under various conditions. Within the same material, the structures and evolution of high-temperature regimes may show high similarity if the shock strength and temperature threshold are chosen appropriately. For process similarity in materials with high porosity, the required temperature threshold increases parabolically with the impact velocity. When the porosity becomes lower, the increasing rate becomes higher. For process similarity in different materials, the required temperature threshold and the porosity follow a power-law relationship in some range.
At a magic relative twist angle, magic angle twisted bilayer graphene (MATBG) has an octet of flat bands that can host strong correlation physics when partially filled. A key theoretical discovery in MATBG is the exis...
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The paper investigates theoretically the optimization of the doped ablator layers for the plastic ignition capsule. The high-resolved one-dimensional implosion simulations show that the inner pure CFI layer of the Si-...
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The paper investigates theoretically the optimization of the doped ablator layers for the plastic ignition capsule. The high-resolved one-dimensional implosion simulations show that the inner pure CFI layer of the Si-doped design is excessively preheated by the hard x-ray, leading to the unstable ablator-fuel interface compared to the Ge-doped capsule. This is because that the Si K-shell absorption edge （1.8 keV） is higher than the Ge L-edge （1.3 keV）, and Si dopant makes more hard x-ray penetrate through the doped ablator layers to preheat the inner pure CH layer. So an optimization of the doped ablator layers （called ＂Si/Ge capsule＂） is performed： an Si-doped CH layer is placed next to the outer pure CH layer to keep the high implosion velocity; next to the Si-doped layer is a thin Ge-doped layer, in order to absorb the hard x-ray and protect the inner undoped CH-layer from excessively preheating. The simulations show that the Si/Ge capsule can effectively improve hydrodynamic stability at the ablator-fuel interface while keeping the high implosion velocity.
For any fixed Alfvén number, the local well-posedness is proved for the equations of threedimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth...
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For any fixed Alfvén number, the local well-posedness is proved for the equations of threedimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfvén number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfvén number goes to zero.
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian *** equations are discretized by the ...
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In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian *** equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG *** multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other *** first,a linear Riemann solver is applied to calculate the numerical ？ux at the *** examples show that there is some oscillation in the vicinity of the *** a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation *** single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the ce...
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A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.
The validity of single-fluid model in inertial confinement fusion simulations is studied by comparing the results of the multi- and single-fluid models. The multi-fluid model includes the effects of collision and inte...
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The validity of single-fluid model in inertial confinement fusion simulations is studied by comparing the results of the multi- and single-fluid models. The multi-fluid model includes the effects of collision and interpenetration between fluid species. By simulating the collision of fluid species, steady-state shock propagation into the thin DT gas and expansion of hohlraum Au wall heated by lasers, the results show that the validity of single-fluid model is strongly dependent on the ratio of the characteristic length of the simulated system to the particle mean free path. When the characteristic length L is one order larger than the mean free path A, the single-fluid model＇s results are found to be in good agreement with the multi-fluid model＇s simulations, and the modeling of single-fluid remains valid. If the value of L/A is lower than 10, the interpenetration between fluid species is significant, and the single-fluid simulations show some unphysical results; while the multi-fluid model can describe well the interpenetration and mix phenomena, and give more reasonable results.
Using density functional theory simulations, this study introduces Petal-Graphyne (PLG), a novel multi-ring metallic structure composed of 4-, 8-, 10-, and 16-membered rings. Its structural, electronic, and lithium/so...
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