Development of new numerical integration schemes of.multiscale coarse-graining methods

Abstract : This thesis is about the development and analysis of numerical schemes forthe integration of the Dissipative Particle Dynamics with Energy conservation. A presentation and a weak convergence analysis of existing schemes is performed, as well as the introduction and a similar analysis of two new straightforwardly parallelizable schemes. The energy preservation properties of all these schemes are studied followed by a comparative study of their biases on the estimation of the average values of physical observables on equilibrium simulations. The schemes are then tested on shock simulations of DPDE fluids, where we show that our schemes bring an improvement on the accuracy of the description of the behavior of such systems compared to existing straightforwardly parallelizable schemes. Finally, we present an attempt at accelerating a reference DPDE integration scheme on sequential simulations
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Ahmed Homman. Development of new numerical integration schemes of.multiscale coarse-graining methods. General Mathematics [math.GM]. Université Paris-Est, 2016. English. ⟨NNT : 2016PESC1040⟩. ⟨tel-01343764v2⟩

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