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We present two numerical experiments concerning application of a recent outflow boundary condition proposal, by Dong et al. (J Comput Phys 261:83-105, 1), to discontinuous Galerkin method (DG) solution of incompressible laminar flows. This new boundary condition (BC) is tailored out for outflow boundaries and its rationale is based on energy influx control at this boundary surface, as described in Braack and Mucha (J Comput Math 32(5):507-521, 2). The authors applied it to various incompressible test-flow examples in a spectral and classic finite-element contexts, and a major result achieved by them was this new outflow boundary's approach allows us to significantly reduce computational domain size without generating significant errors. Accordingly, due to its already known capabilities and established mathematical basis, it is a natural issue to ask about the DG behaviour over this all-useful achievement. In this work, the DG method is tested in two different flow instances: (1) Kovasznay flow, where convergence rates are measured and (2) laminar incompressible flow around cylinder inside rectangular channel. In this case, drag and lift coefficients are computed, further of the dimensionless Strouhal number. Conclusions are traced to show the readiness of DG to embody this new boundary condition technique. Keywords High-order method Á Outflow boundary condition Á Unstructured grids Á Incompressible Navier-Stokes equations Á Discontinuous Galerkin Method

In this work, a coupled fluid-structure problem is approached, comparing the result with the modal analysis of a structure. The objective of this work is to analyze the physical phenomenon of fluid-structure interaction of a flexible structure. For this, the coupled problem solved using an Arbitrary Lagrangean-Eulerian (ALE) approach. As support for solving the mathematical equations of coupled problem, ANSYS® physical analysis software was used. An experimental modal analysis, using the Rational Fractional Polynomial method was developed for a small scale steel structure, and the result of this was compared with the result obtained from the model simulated in the software. Their vibration modes and natural frequencies obtained by numerical modeling were validated experimentally. Whit the numerical modeling of the modal analysis of a structure experimentally validated, attempted to analyze the dynamic behavior of the structure when it is subjected to a load due to a fluid-flow through a coupled fluid-structure problem. The results presented in this work show that the structure subjected to loads due to the fluid-flow, moves according to its vibration modes.

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The phenomenon of ablation is a process of thermal protection with several applications, mainly, in mechanical and aerospace engineering. Ablative thermal protection is applied using special materials (named ablative materials) externally on the surface of a structure in order to isolate it against thermal effects. The ablative phenomenon is a complex process involving phase changes with partial or total loss of the material. So the position of the boundary is initially unknown. The governing equations of the process form a non-linear system of coupled partial differential equations. The one-dimensional analysis of an ablative process on the plate is performed by using the generalized integral transform technique – GITT for solution of the system of governing equations. By application of this solution technique, the system of partial differential equations is transformed into a system of infinite ordinary differential equations that can be solved after the truncation of that system by numerical techniques codes available. The plate of finite thickness at constant properties is subjected to a time-dependent prescribed radiation heat flux at one face, initially with a uniform temperature T0, and insulated on the other face. After an initial heating period, ablation starts at the heated surface through melting and continuous removal of the plate material. The results of interest are the thickness and the loss rate of the ablative material. The obtained results are compared with available results from other solution techniques in the literature.

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