International Journal for Numerical Methods in Fluids

Zhang, Jiexing; Han, Ruoyu; Ni, Guoxi

doi: 10.1002/fld.5228pmid: N/A

We propose a high‐order curvilinear Lagrangian finite element method for shallow water hydrodynamics. This method falls into the high‐order Lagrangian framework using curvilinear finite elements. We discretize the position and velocity in continuous finite element spaces. The high‐order finite element basis functions are defined on curvilinear meshes and can be obtained through a high‐order parametric mapping from a reference element. Considering the variational formulation of momentum conservation, the global mass matrix is independent of time due to the use of moving finite element basis functions. The mass conservation is discretized in a pointwise manner which is referred to as strong mass conservation. A tensor artificial viscosity is introduced to deal with shocks, meanwhile preserving the symmetry property of solutions for symmetric flows. The generic explicit Runge–Kutta method could be adopted to achieve high‐order time integration. Several numerical experiments verify the high‐order accuracy and demonstrate good performances of using high‐order curvilinear elements.

Cheng, Jian; Zhang, Fan

doi: 10.1002/fld.5230pmid: N/A

In this work, we present a two‐dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under‐resolved regions. Several typical two‐dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two‐material flows.

Chandra, Priyanka; Das, Raja

doi: 10.1002/fld.5229pmid: N/A

The Levenberg–Marquardt algorithm with back‐propagated neural network (BLM‐NN) based on machine learning is used in a dynamic fashion in this study to examine the 2D boundary layer flow of a nanofluid comprising gyrotactic microorganisms flowing across a stretchable vertically inclined surface (NGM‐ISSFM), immersed in a porous medium. An extensively verified finite‐element method (FEM) is used to produce the reference data set for BLM‐NN by altering five crucial parameters of the flow model in MATLAB. The main objective of this innovative approach is to minimize longer execution times (for larger number of elements) and more expensive digital computer requirements that are the key barriers to opting the FEM, and in order to obtain the entire function instead of the discrete solution that other numerical methods typically produce. To estimate the NGM‐ISSFM model's result for diverse scenario, BLM‐NN is trained, tested, and validated. Several BLM‐NN implementations using MSE‐based indices have shown the performance's veracity and validity through descriptive statistics. The results show that when the Prandtl number increases, the temperature profile and density profile of microorganisms fall dramatically, implying that a fluid with a low Prandtl number is required to enhance the rate of heat transmission.

Li, Weizhao; Pandare, Aditya K.; Luo, Hong; Bakosi, Jozsef; Waltz, Jacob

doi: 10.1002/fld.5231pmid: N/A

A novel p‐adaptive discontinuous Galerkin (DG) method has been developed to solve the Euler equations on three‐dimensional tetrahedral grids. Hierarchical orthogonal basis functions are adopted for the DG spatial discretization while a third order TVD Runge‐Kutta method is used for the time integration. A vertex‐based limiter is applied to the numerical solution in order to eliminate oscillations in the high order method. An error indicator constructed from the solution of order (p)$$ (p) $$ and (p−1)$$ \left(p-1\right) $$ is used to adapt degrees of freedom in each computational element, which remarkably reduces the computational cost while still maintaining an accurate solution. The developed method is implemented with under the Charm++ parallel computing framework. Charm++ is a parallel computing framework that includes various load‐balancing strategies. Implementing the numerical solver under Charm++ system provides us with access to a suite of dynamic load balancing strategies. This can be efficiently used to alleviate the load imbalances created by p‐adaptation. A number of numerical experiments are performed to demonstrate both the numerical accuracy and parallel performance of the developed p‐adaptive DG method. It is observed that the unbalanced load distribution caused by the parallel p‐adaptive DG method can be alleviated by the dynamic load balancing from Charm++ system. Due to this, high performance gain can be achieved. For the testcases studied in the current work, the parallel performance gain ranged from 1.5× to 3.7×. Therefore, the developed p‐adaptive DG method can significantly reduce the total simulation time in comparison to the standard DG method without p‐adaptation.