Phenomenological study: bilingual teaching classroom of Malaysian community colleges

The study of bilingual teaching classroom of Malaysian community colleges was designed for developing a brand new environment of teaching in a classroom. It was also to find the main factors that lead to this crucial phenomenon of bilingual classroom. This study has never been conducted among the academicians of community colleges and this is the first study invented by the researcher in order to help in creating new environment of teaching in a bilingual classroom and also to equip learners with good command of English language as to produce trainers who are proficient in the language. The targeted respondents of this study were several course content instructors from several different programs of Malaysian community colleges. Students from semester four undertaking certificate courses from various disciplines of studies were also involved in this research. Non-structured interviews, non-participant observation and note taking were the methods used in this research. The result indicates various answers given by the respondents from the interviews. The needs of the language for each classroom are highly depend on the teachers’ competencies of the language used instead of the learners’ needs. In a nutshell, the bilingual teaching classroom of community colleges can be evaded by practicing better approaches and methods in teaching

Phenomenological study: bilingual teaching classroom of Malaysian community colleges

The study of bilingual teaching classroom of Malaysian community colleges was designed for developing a brand new environment of teaching in a classroom. It was also to find the main factors that lead to this crucial phenomenon of bilingual classroom. This study has never been conducted among the academicians of community colleges and this is the first study invented by the researcher in order to help in creating new environment of teaching in a bilingual classroom and also to equip learners with good command of English language as to produce trainers who are proficient in the language. The targeted respondents of this study were several course content instructors from several different programs of Malaysian community colleges. Students from semester four undertaking certificate courses from various disciplines of studies were also involved in this research. Non-structured interviews, non-participant observation and note taking were the methods used in this research. The result indicates various answers given by the respondents from the interviews. The needs of the language for each classroom are highly depend on the teachers’ competencies of the language used instead of the learners’ needs. In a nutshell, the bilingual teaching classroom of community colleges can be evaded by practicing better approaches and methods in teaching

More efficient time integration for Fourier pseudo-spectral DNS of incompressible turbulence

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge--Kutta pair of Bogacki \& Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2x-10x for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy

Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

Proper orthogonal decomposition closure models for fluid flows: Burgers equation

This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical simulation of the Burgers equation. This simplified setting represents just the first step in the investigation of the new closure models. It allows a thorough assessment of the performance of the new models, including a parameter sensitivity study. Two challenging test problems displaying moving shock waves are chosen in the numerical investigation. The closure models and a standard Galerkin POD reduced order model are benchmarked against the fine resolution numerical simulation. Both numerical accuracy and computational efficiency are used to assess the performance of the models

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm