TWO-GRID WEAK GALERKIN METHOD FOR SEMILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, we investigate a two-grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semi-linear elliptic equation on the coarse mesh with mesh size H, then, we use the coarse mesh solution as a initial guess to linearize the semilinear equation on the fine mesh, i.e., on the fine mesh (with mesh size $h$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u has sufficient regularity and $h=H^2$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.

Inquisition of Electro-Magnetic Riga Plate for Laminar Flow

The probation is made to study the stagnation point flow of non-Newtonian fluid for Riga plate. Electric potential and magnetic flux density with time dependent flow is examined. Mesh for electric potential, magnetic flux, laminar flow with physics controlled fine, finer and extra finer option is also represented in details. Inquisition is solved in COMSOL Multi-physics 5.4 to obtain the results of surface magnitude, counter, table surface, magnetic flux, electric potential and coarse mesh for velocity, pressure, magnetic and electric fields. Coarse mesh of electric insulation and magnetic flux of the geometry is created with 6067, 18688 domain elements and 901, 1448 boundary elements. Tables for velocity surface, mesh domain, quadrilateral and triangular elements are also presented. Obtained results are discussed with graphs and tables in details.

A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

On locally embedded two-scale solution for wall-bounded turbulent flows

Recent findings on wall-bounded turbulence have prompted a new impetus for modelling development to capture and resolve the Reynolds-number-dependent influence of outer flow on near-wall turbulence in terms of the ‘foot-printing’ of the large-scale coherent structures and the scale-interaction associated ‘modulation’. We develop a two-scale method to couple a locally embedded near-wall fine-mesh direct numerical simulation (DNS) block with a global coarser mesh domain. The influence of the large-scale structures on the local fine-mesh block is captured by a scale-dependent coarse–fine domain interface treatment. The coarse-mesh resolved disturbances are directly exchanged across the interface, while only the fine-mesh resolved fluctuations around the coarse-mesh resolved variables are subject to periodic conditions in the streamwise and spanwise directions. The global near-wall coarse-mesh region outside the local fine-mesh block is governed by the augmented flow governing equations with forcing source terms generated by upscaling the space–time-averaged fine-mesh solution. The validity and effectiveness of the method are examined for canonical incompressible channel flows at several Reynolds numbers. The mean statistics and energy spectra are in good agreement with the corresponding full DNS data. The results clearly illustrate the ‘foot-printing’ and ‘modulation’ in the local fine-mesh block. Noteworthy also is that neither spectral-gap nor scale-separation is assumed, and a smooth overlap between the global-domain and the local-domain energy spectra is observed. It is shown that the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for the conventional fully wall-resolved large-eddy simulation (LES) to $O(Re)$ for the present locally embedded two-scale LES.

An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow

We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC (energy, momentum, and angular momentum conserving) formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC formulation has proved to be a useful formulation because it conserves energy, momentum and angular momentum even when the divergence constraint is only weakly enforced. However, it is still a NSE formulation and so cannot resolve higher Reynolds number flows without very fine meshes. By carefully introducing regularization into the EMAC formulation, we create a model more suitable for coarser mesh computations but that still conserves the same quantities as EMAC, i.e., energy, momentum, and angular momentum. We show that EMAC-Reg, when semi-discretized with a finite element spatial discretization is well-posed and optimally accurate. Numerical results are provided that show EMAC-Reg is a robust coarse mesh model.

Effect of Mesh Topologies to Predict Cooling Effect on Evaporative Cooling Duct

This paper examines the effect of different mesh types on a numerical study of evaporative cooling in the chimney. This research is a follow-up study from previous research. The test specimen used is an evaporative chimney design with the addition of a nozzle arrangement in it. The main focus of this research is the study of mesh refinement, namely by applying structured mesh during the simulation process. Three types of mesh with different levels of fineness were used for the specimens. They are coarse ( mesh A), medium (mesh B), and fine (mesh C). In addition to differences in mesh, research was also carried out with variations in the level of relative humidity (RH). The RH levels used are 5, 10, and 15%. Two main parameters of evaporative cooling performance are airflow distribution and temperature drop in the chimney. Method for measuring the distribution of airflow and temperature drop in the chimney by making five planes with different heights. The results showed that the simulation with mesh B produced a good agreement data with previous studies than mesh A and C. The RH level that generated the most optimal cooling is found at 5% RH.