Methods based on Monte Carlo solutions of the transport equation for the joint probability density function (pdf) of scalars are considered to be among the most promising approaches for modeling turbulent reactive flows. For the treatment of convection and diffusion two approaches are well established...
We sum up some new results concerning the mathematical structure of Lagrangian systems of conservation laws. These results include the assumption of Galilean invariance in the hypothesis and extend the classical symmetrization theorem of S. K. Godunov. Based on this representation theorem it is straigh...
An efficient thermal-structural numerical solver for Additive Manufacturing has been developed based on a modified Lagrangian approach to solve the energy conservation equations in differential form. The heat transfer is modeled using the finite differen
We may then use cutoff functions to get an approximate solution to (52) by patching together local solutions using cutoff functions, as in [25, Lemma 2.6] and [15, Section IV.7]. Then, by restricting the time interval to T<ϵ (where ϵ depends only on the coefficients of (52) ...
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h and −h are all convex. Thus h should be linear in x. 2.2 Linear programs We will study problems of the form 1 minimize c ⊤ x : Ax ≤ b , x ≥ 0 where x and c are n-vectors, b is a m-vector and A is a m × n matrix. Such problems are also written out in the...
Nonetheless, the Lagrangian approach is diffusion-free and highly parallelizable as all particles are advected independently. In addition, the Lagrangian method is recognized to be CFL-free (Qiu and Shu, 2011). Read full articleView PDF 27th European Symposium on Computer Aided Process Engineering ...
problems for hybrid systems in an optimal control context, which supports theoretically the use of publicly available numerical tools [17] for hybrid reachability calculations. The proposed formulation is entirely based on optimal control and the properties of the hybrid system executions, and as such...
For a suitable exponential kernel ωη of class C2, we present theoretical and numerical evidence that the limit of solutions to the nonlocal equation coincides with the unique entropy-admissible solution of the scalar conservation law ρt+(ρmv(q))x=0. It should be emphasized that hypotheses...
GOAL #5: In the same section, we look for Gaussian initial particular solutions for the same quantum PDF. 6. GOAL #6: In Sect. 6 applications of the GLP-approach are considered, which consist in the explicit construction of particular polynomial solutions of the quantum Hamilton–Jacobi equa...