International Journal for Numerical Methods in Fluids最新文献

{"title":"Enhanced conservative phase field method for moving contact line problems","authors":"Mingguang Shen,&nbsp;Ben Q. Li","doi":"10.1002/fld.5286","DOIUrl":"10.1002/fld.5286","url":null,"abstract":"<p>The traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature-driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half-staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 7","pages":"1215-1229"},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On robust boundary treatments for wall-modeled LES with high-order discontinuous finite element methods","authors":"Yuma Fukushima,&nbsp;Takanori Haga","doi":"10.1002/fld.5281","DOIUrl":"10.1002/fld.5281","url":null,"abstract":"<div>\u0000 \u0000 <p>To robustly and accurately simulate wall-bounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wall-modeled large-eddy simulation (WMLES) coupled with a high-order flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in high-order discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with under-resolved grids, is the use of a modal filter only in the wall-normal direction of wall-adjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <msub>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>≈</mo>\u0000 <mn>5200</mn>\u0000 </mrow>\u0000 <annotation>$$ R{e}_{tau}approx 5200 $$</annotation>\u0000 </semantics></math>) shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, non-equilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <msub>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>≈</mo>\u0000 <mn>37</mn>\u0000 <mo>,</mo>\u0000 <mn>000</mn>\u0000 </mrow>\u0000 <annotation>$$ R{e}_happrox 37,000 $$</annotation>\u0000 </semantics></math>), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using high-order DFEMs.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 7","pages":"1170-1193"},"PeriodicalIF":1.8,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simulation of fluid-structure interaction using the boundary data immersion method with adaptive mesh refinement","authors":"Yuan Wang,&nbsp;Wei Ge","doi":"10.1002/fld.5283","DOIUrl":"10.1002/fld.5283","url":null,"abstract":"<div>\u0000 \u0000 <p>The fluid-structure interaction is simulated using the boundary data immersion method. As the fluid-structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mo>.</mo>\u0000 <mn>67</mn>\u0000 </mrow>\u0000 <annotation>$$ =2.67 $$</annotation>\u0000 </semantics></math> and Re <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>=</mo>\u0000 <mn>1482</mn>\u0000 </mrow>\u0000 <annotation>$$ =1482 $$</annotation>\u0000 </semantics></math>, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 7","pages":"1156-1169"},"PeriodicalIF":1.8,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local discontinuous Galerkin method coupled with the implicit-explicit Runge–Kutta method for the time-dependent micropolar fluid equations","authors":"Mengqi Li,&nbsp;Demin Liu","doi":"10.1002/fld.5282","DOIUrl":"10.1002/fld.5282","url":null,"abstract":"<p>In this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicit-explicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicit-explicit RK method are properly combined to construct the expected third-order method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 7","pages":"1137-1155"},"PeriodicalIF":1.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A centered limited finite volume approximation of the momentum convection operator for low-order nonconforming face-centered discretizations","authors":"A. Brunel,&nbsp;R. Herbin,&nbsp;J.-C. Latché","doi":"10.1002/fld.5276","DOIUrl":"10.1002/fld.5276","url":null,"abstract":"&lt;p&gt;We propose in this article a discretization of the momentum convection operator for fluid flow simulations on quadrangular or generalized hexahedral meshes. The space discretization is performed by the low-order nonconforming Rannacher–Turek finite element: the scalar unknowns are associated with the cells of the mesh while the velocities unknowns are associated with the edges or faces. The momentum convection operator is of finite volume type, and its expression is derived, as in MUSCL schemes, by a two-step technique: &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ (i) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; computation of a tentative flux, here, with a centered approximation of the velocity, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ (ii) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; limitation of this flux using monotonicity arguments. The limitation procedure is of algebraic type, in the sense that its does not invoke any slope reconstruction, and is independent from the geometry of the cells. The derived discrete convection operator applies both to constant or variable density flows and may thus be implemented in a scheme for incompressible or compressible flows. To achieve this goal, we derive a discrete analogue of the computation &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mtext&gt;div&lt;/mtext&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"1104-1135"},"PeriodicalIF":1.8,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate inner solvers for block preconditioning of the incompressible Navier–Stokes problems discretized by isogeometric analysis","authors":"Jiří Egermaier,&nbsp;Hana Horníková","doi":"10.1002/fld.5280","DOIUrl":"10.1002/fld.5280","url":null,"abstract":"<p>We deal with efficient numerical solution of the steady incompressible Navier–Stokes equations (NSE) using our in-house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle-point linear systems using preconditioned Krylov subspace methods. Based on our comparison of ideal versions of several state-of-the-art block preconditioners for linear systems arising from the IgA discretization of the incompressible NSE, suitable candidates have been selected. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within these preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination. For this purpose, we compare convergence properties of the selected solution approaches for problems with different viscosity values, mesh refinement levels and discretization bases.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"1078-1103"},"PeriodicalIF":1.8,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enforcing accurate volume conservation in VOF-based long-term simulations of turbulent bubble-laden flows on coarse grids","authors":"Elias Trautner,&nbsp;Josef Hasslberger,&nbsp;Paolo Cifani,&nbsp;Markus Klein","doi":"10.1002/fld.5279","DOIUrl":"10.1002/fld.5279","url":null,"abstract":"<p>This study proposes two different strategies to enforce accurate volume conservation in volume-of-fluid (VOF)-based simulations of turbulent bubble-laden flows on coarse grids. It is demonstrated that, without a correction, minimal volume errors on a time-step level, caused by the under-resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long-term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non-divergence-free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi-identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"1057-1077"},"PeriodicalIF":1.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"High-resolution mapping type WENO-Z schemes for solving compressible flow","authors":"Shujiang Tang,&nbsp;Mingjun Li","doi":"10.1002/fld.5275","DOIUrl":"10.1002/fld.5275","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper presents a new WENO-Z scheme (WENO-MZ) that incorporates a mapping function to enhance the weights of the less smooth sub-stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub-stencil to the smooth stencil. In addition, we present the WENO-MD scheme, which is a further development of the WENO-MZ scheme that incorporates a modifier function. The WENO-MD scheme shows improvements over the WENO-MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub-stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO-JS, WENO-Z, WENO-M, WENO-D, and WENO-AIM, and also lead to significant computational time savings compared to WENO-M and WENO-AIM.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"1031-1056"},"PeriodicalIF":1.8,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conservative solution transfer between anisotropic meshes for time-accurate hybridized discontinuous Galerkin methods","authors":"Tomáš Levý,&nbsp;Georg May","doi":"10.1002/fld.5278","DOIUrl":"10.1002/fld.5278","url":null,"abstract":"<p>We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. In particular, we focus on a coupling of the solution process for unsteady problems with our anisotropic mesh refinement framework. The goal is to properly resolve all relevant unsteady features with the smallest possible number of mesh elements, and hence to reduce the computational cost of numerical simulations while maintaining its accuracy. A crucial step is then to transfer the numerical solution between two meshes, as the anisotropic mesh adaptation is producing highly skewed, non-nested sequences of triangular grids. For this purpose, we adopt the Galerkin projection for the HDG solution transfer as it preserves the conservation of physically relevant quantities and does not compromise the accuracy of high-order method. We present numerical experiments verifying these properties of the anisotropically adaptive HDG method.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"1011-1030"},"PeriodicalIF":1.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5278","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Predicting aerosol transmission in airplanes: Benefits of a joint approach using experiments and simulation","authors":"Christian Leithäuser,&nbsp;Victor Norrefeldt,&nbsp;Elisa Thiel,&nbsp;Michael Buschhaus,&nbsp;Jörg Kuhnert,&nbsp;Pratik Suchde","doi":"10.1002/fld.5277","DOIUrl":"10.1002/fld.5277","url":null,"abstract":"<p>We investigate the transmission of aerosol particles in an airplane cabin with a joint approach using experiments and simulation. Experiments were conducted in a realistic aircraft cabin with heated dummies acting as passengers. A Sheffield head with an aerosol generator was used to emulate an infected passenger and particle numbers were measured at different locations throughout the cabin to quantify the exposure of other passengers. The same setting was simulated with a computational fluid dynamics model consisting of a Lagrange continuous phase for capturing the air flow, coupled with a Lagrange suspended discrete phase to represent the aerosols. Virtual measurements were derived from the simulation and compared with the experiments. Our main results are: the experimental setup provides good measurements well suited for model validation, the simulation does correctly reproduce the fundamental mechanisms of aerosol dispersion and simulations can help to improve the understanding of aerosol transmission for example by visualizing particle distributions. Furthermore, with findings from the simulation it was possible to crucially improve the experimental setup, proving that feedback between the numerical and the hardware world is indeed beneficial.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"96 6","pages":"991-1010"},"PeriodicalIF":1.8,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139981645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}