The LifeV library: engineering mathematics beyond the proof of concept

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis. Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility

A high order compact scheme for hypersonic aerothermodynamics

A novel high order compact scheme for solving the compressible Navier-Stokes equations has been developed. The scheme is an extension of a method originally proposed for solving the Euler equations, and combines several techniques for the solution of compressible flowfields, such as upwinding, limiting and flux vector splitting, with the excellent properties of high order compact schemes. Extending the method to the Navier-Stokes equations is achieved via a Kinetic Flux Vector Splitting technique, which represents an unusual and attractive way to include viscous effects. This approach offers a more accurate and less computationally expensive technique than discretizations based on more conventional operator splitting. The Euler solver has been validated against several inviscid test cases, and results for several viscous test cases are also presented. The results confirm that the method is stable, accurate and has excellent shock-capturing capabilities for both viscous and inviscid flows

Kepimpinan instruksional dalam peningkatan pengajaran dan pembelajaran yang berkesan dalam kalangan pensyarah

Kajian ini meneroka amalan kepimpinan instruksional pensyarah sebagai pemimpin pengajaran dan pembelajaran di Kolej KemahiranTinggi MARA Sri Gading, Kolej Kemahiran Tinggi MARA Ledang dan Kolej Kemahiran Tinggi Masjid Tanah. Pensyarah yang dipilih sebagai kepimpinan instruksional adalah terdiri daripada Timbalan Pengarah HEA, Ketua Jabatan, Ketua Program, Ketua Unit dan Penyelaras Kursus yang berasaskan empat amalan pengurusan instruksional iaitu merangka matlamat pengajaran dan pembelajaran, pemantauan kurikulum dengan pengajaran dan pembelajaran, mengekalkan pemantauan kurikulum dengan pengajaran dan pembelajaran, dan berdasarkan sokongan pembelajaran dengan pengajaran dan pembelajaran. Kajian deskriptif ini dijalankan secara tinjauan keatas 108 responden dari tiga lokasi kajian dengan menggunakan borang soal selidik. Pengumpulan data secara mengedarkan soal selidik mengandungi bahagian demografi dan 4 bahagian mengandungi 24 item kajian kepada semua responden. Analisis data berasaskan perisian SPSS versi 20 dalam bentuk statistik deskriptif iaitu nilai min, sisihan piawai, ujian-t sampel bebas dan anova satu hala. Hasil kajian ini semuanya menunjukkan pada tahap tinggi dalam kepimpinan instruksional berdasarkan pemantauan kurikulum pembelajaran. Ujian-t menunjukkan tidak terdapat perbezaan yang signifikan antara tahap kepimpinan instruksional dengan jantina dan ujian anova satu hala menunjuk tidak terdapat pebezaan yang signifikan antara status jawatan dengan kepimpinan instruksional. Dapatan kajian ini, menunjukkan bahawa pensyarah KKTM mempunyai pengetahuan dan kemahiran yang baik dalam kepimpinan instruksional dalam pengajaran dan pembelajaran

On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations

Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms that are specific to meshfree methods have often been overlooked. In this paper, we study the drawbacks of conventionally used meshfree Generalized Finite Difference Method~(GFDM) schemes for Lagrangian incompressible Navier-Stokes equations, both operator splitting schemes and monolithic schemes. The major drawback of most of these schemes is inaccurate local approximations to the mass conservation condition. Further, we propose a new modification of a commonly used monolithic scheme that overcomes these problems and shows a better approximation for the velocity divergence condition. We then perform a numerical comparison which shows the new monolithic scheme to be more accurate than existing schemes

Aerodynamics of thrust vectoring by Navier-Stokes solutions

Induced aerodynamics from thrust vectoring are investigated by a computational fluid dynamic method. A thin-layer Reynolds-averaged Navier-Stokes code with multiblock capability is used. Jet properties are specified on the nozzle exit plane to simulate the jet momentum. Results for a rectangular jet in a cross flow are compared with data to verify the code. Further verification of the calculation is made by comparing the numerical results with transonic data for a wing-body combination. Additional calculations were performed to elucidate the following thrust vectoring effects: the thrust vectoring effect on shock and expansion waves, induced effects on nearby surfaces, and the thrust vectoring effect on the leading edge vortex

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure

An adaptive fixed-mesh ALE method for free surface flows

In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version