Analysis of a constant-coefficient pressure equation method for fast computations of two-phase flows at high density ratios

An analysis of a modified pressure-correction formulation for fast simulations of fully resolved incompressible two-phase flows has been carried out. By splitting of the density weighted pressure gradient, the pressure equation is reduced to a constant-coefficient Poisson equation, for which efficient linear solvers can be used. While the gain in speed-up is well documented, the error introduced by the temporal extrapolation of the pressure gradient requires further investigations. In this paper it is shown that the modified pressure equation can lead to unphysical pressure oscillations and large errors. By appropriately combining the extrapolated pressure gradient with a matching volume fraction gradient grid convergence at high density ratios could be recovered. The cases of a one-dimensional front and a sphere translating at uniform velocity were first considered, allowing to decouple the pressure equation from the momentum equation. Subsequently, the case of a rising bubble in an upflow is analysed for which the full set of governing equations is solved. The pressure jump extrapolation error has been found dependent on the density ratio and the CFL number. Ultimately, the gain in the computational time, made possible by the use of fast Poisson solvers, should be weighted by the additional computational time the reduction of the aforementioned error may require

Building a map of the breast cancer proteome - Strategies to increase coverage

Amongst the various –omics sciences, proteomics has the highest potential for functional characterization and consequently can contribute significantly to the field of cancer research. In particular, the focus of this thesis is on breast cancer. Alas, since state-of-the-art technologies cannot meet the complexity of upper eukaryotic proteomes, a complete resolution of clinical samples is still unachievable. Comprehensive mapping of proteins involved in cancer and of their PTMs is proposed in this thesis as a general strategy to increase the output of mass-spectrometry based proteomics. Different approaches to improve the coverage of this map are proposed: optimization of sample fractionation, focusing on difficult sub-proteomes, targeting of specific biological processes and optimization of data analysis. A combination of these approaches will provide a growing collection of empirical MS-spectra, which will enhance the detection by shotgun proteomics and facilitate the transition towards the development of targeted assays

An efficient geometric method for incompressible hydrodynamics on the sphere

We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a tridiagonal splitting of the discrete spherical Laplacian combined with highly optimized, scalable numerical algorithms. For time-stepping, we adopt a recently developed isospectral integrator able to preserve the geometric structure of Euler's equations, in particular conservation of the Casimir functions. To overcome previous computational bottlenecks, we formulate the matrix Lie algebra basis through a sequence of tridiagonal eigenvalue problems, efficiently solved by well-established linear algebra libraries. The same tridiagonal splitting allows for computation of the stream matrix, involving the inverse Laplacian, for which we design an efficient parallel implementation on distributed memory systems. The resulting overall computational complexity is $\mathcal{O}(N^3)$ per time-step for $N^2$ spatial degrees of freedom. The dominating computational cost is matrix-matrix multiplication, carried out via the parallel library ScaLAPACK. Scaling tests show approximately linear scaling up to around $2500$ cores for the matrix size $N=4096$ with a computational time per time-step of about $0.55$ seconds. These results allow for long-time simulations and the gathering of statistical quantities while simultaneously conserving the Casimir functions. We illustrate the developed algorithm for Euler's equations at the resolution $N=2048$

Data-driven stochastic Lie transport modelling of the 2D Euler equations

Stochastic modelling of coarse-grid SPDEs of the two-dimensional Euler equations, in the framework of Stochastic Advection by Lie Transport (SALT) [Cotter et al, 2019], is considered. We propose and assess a number of models as stochastic forcing. The latter is decomposed in terms of a deterministic basis (empirical orthogonal functions) multiplied by temporal traces, here regarded as stochastic processes. In particular, we construct the stochastic forcing from the probability density functions (pdfs) and the correlation times obtained from a fine-grid data set. We perform uncertainty quantification tests to compare the different stochastic models. In particular, comparison to Gaussian noise, in terms of ensemble mean and ensemble spread, is conducted. Reduced uncertainty is observed for the developed models. On short timescales, such as those used for data assimilation [Cotter et al, 2020a], the former models show a reduced ensemble mean error and a reduced spread. Estimating the pdfs yielded stochastic ensembles which rarely failed to capture the reference solution on short timescales, as is demonstrated by rank histograms. Overall, introducing correlation into the stochastic models improves the quality of the coarse-grid predictions with respect to white noise.Comment: 14 pages, 10 figure

Data-driven spectral turbulence modelling for Rayleigh–Bénard convection

A data-driven turbulence model for coarse-grained numerical simulations of two-dimensional Rayleigh–Bénard convection is proposed. The model starts from high-fidelity data and is based on adjusting the Fourier coefficients of the numerical solution, with the aim of accurately reproducing the kinetic energy spectra as seen in the high-fidelity reference findings. No assumptions about the underlying partial differential equation or numerical discretization are used in the formulation of the model. We also develop a constraint on the heat flux to guarantee accurate Nusselt number estimates on coarse computational grids and high Rayleigh numbers. Model performance is assessed in coarse numerical simulations at Ra=1010 . We focus on key features including kinetic energy spectra, wall-normal flow statistics and global flow statistics. The method of data-driven modelling of flow dynamics is found to reproduce the reference kinetic energy spectra well across all scales and yields good results for flow statistics and average heat transfer, leading to computationally cheap surrogate models. Large-scale forcing extracted from the high-fidelity simulation leads to accurate Nusselt number predictions across two decades of Rayleigh numbers, centred around the targeted reference at Ra=1010

Towards LES of bubble-laden channel flows: sub-gridscale closures for momentum advection

This paper presents an a-posteriori assessmentof different LES sub-grid scale closures for momentumadvection in the context of bubble-laden channelflows. The numerical approach is based on theVolume-of-Fluid method in combination with the onefluidformulation of the incompressible Navier-Stokesequations. To study the behavior of different subgridscale models, a turbulent bubble-laden downflowchannel is simulated at a friction Reynolds number ofRe = 590. The setup is chosen such that the bubblesare nearly spherical, but mildly wobbling. Both functionalmodels of eddy viscosity type and scale similaritytype models are used to close the sub-grid scalestresses. The results are compared to a direct numericalsimulation of the same setup. It is found that thestream-wise volumetric flow rate depends strongly onthe closure model as well as the grid resolution. Whilesome models lead to an improvement compared to theLES without an explicit model, the comparably dissipativenature of the QUICK scheme prevents a clearassessment of some more advanced modeling strategies

LKS Asam Basa Berbasis Pendekatan Ilmiah Dalam Meningkatkan KPS Berdasarkan Kognitif Siswa

This research aimed to describe the effectiveness of scientific approach based student worksheets in improving science process skills (SPS) insight from student\u27s cognitive. The method of this research was quasi experimental with 2x2 factorial design. The population of this research was all students of XI IPA SMAN 15 Bandarlampung on 2016/2017. The sample were XI IPA-4 and the XI IPA 2 which taken by purposive sampling. The data of this study were analyzed by using two ways ANOVA test and t test. The result of this research was no interaction between learning with scientific approach based worksheets and cognitive on SPS; learning process using student worksheets scientific approach was effective to improve SPS; SPS high and low cognitive ability with learning using worksheets Scientific Approach wass higher than conventional worksheets; SPS high cognitive ability was higher than low cognitive ability with learning using worksheets scientific approach. Penelitian ini bertujuan mendeskripsikan efektivitas LKS pendekatan ilmiah dalam meningkatkan KPS berdasarkan kognitif siswa. Metode penelitian menggunakan kuasi eksperimen dengan desain faktorial 2x2. Populasi penelitian seluruh siswa kelas XI IPA di SMAN 15 Bandarlampung tahun 2016/2017. Sampel penelitian ini kelas XI IPA 4 dan kelas XI IPA 2 yang diambil dengan teknik purposive sampling. Data penelitian dianalisis menggunakan uji two ways ANOVA dan uji t. Hasil penelitian menunjukan tidak terdapat interaksi antara pembelajaran menggunakan LKS terhadap KPS berdasarkan kemampuan kognitif, pembelajaran menggunakan LKS pendekatan ilmiah efektif untuk meningkatkan KPS, KPS siswa kognitif tinggi dan rendah dengan pembelajaran menggunakan LKS pendekatan ilmiah lebih tinggi dibandingkan LKS konvensional, KPS siswa kognitif tinggi lebih tinggi dibandingkan KPS siswa kognitif rendah menggunakan LKS pendekatan ilmiah

Towards LES of bubble-laden channel flows: sub-gridscale closures for momentum advection

This paper presents an a-posteriori assessmentof different LES sub-grid scale closures for momentumadvection in the context of bubble-laden channelflows. The numerical approach is based on theVolume-of-Fluid method in combination with the onefluidformulation of the incompressible Navier-Stokesequations. To study the behavior of different subgridscale models, a turbulent bubble-laden downflowchannel is simulated at a friction Reynolds number ofRe = 590. The setup is chosen such that the bubblesare nearly spherical, but mildly wobbling. Both functionalmodels of eddy viscosity type and scale similaritytype models are used to close the sub-grid scalestresses. The results are compared to a direct numericalsimulation of the same setup. It is found that thestream-wise volumetric flow rate depends strongly onthe closure model as well as the grid resolution. Whilesome models lead to an improvement compared to theLES without an explicit model, the comparably dissipativenature of the QUICK scheme prevents a clearassessment of some more advanced modeling strategies