arXiv subjects

Frederico Bolsoni Oliveira

Publications and source records attributed to Frederico Bolsoni Oliveira.

5 recordsLinked to original sources

arXiv2026

A Study of Improved Limiter Formulations for Second-Order Finite Volume Schemes Applied to Unstructured Grids

A general, compact way of achieving second-order in finite-volume numerical methods is to perform a MUSCL-like, piecewise linear reconstruction of flow properties at each cell interface. To avoid the surge of spurious oscillations in the discrete solution, a limiter function is commonly employed. This strategy, however, can add a series of drawbacks to the overall numerical scheme. The present paper investigates this behavior by considering three different limiter formulations in the context of a second-order, finite volume scheme for the simulation of steady, turbulent flows on unstructured meshes. Three limiter formulations are considered: the original Venkatakrishnan limiter, Wang's modification to the Venkatakrishnan limiter and Nishikawa's recently introduced R3 limiter. Three different configurations of the fully-developed, two-dimensional, transonic NACA 0012 airfoil are analyzed, configured with different angles of attack and similar freestream properties. The gas dynamics are modeled using the Reynolds-averaged Navier-Stokes (RANS) equations, where the negative Spalart-Allmaras turbulence model is used to solve the closure problem. All limiters are shown to yield similar results for all configurations of this case, although with different dissipative characteristics, provided their control constants are used within appropriate intervals. The presented numerical results are in good agreement with experimental data available in the literature.

physics.flu-dyn↗

arXiv2026

Study of the Effects of Artificial Dissipation and Other Numerical Parameters on Shock Wave Resolution

The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite-difference schemes are considered: the Beam and Warming implicit approximate factorization algorithm, the original Steger and Warming flux vector splitting algorithm, the van Leer approach on performing the flux vector splitting and two different novel finite-difference interpretations of the Liou AUSM+ scheme. Special focus is given to the shock wave resolution capabilities of each scheme for the solution of an external supersonic inviscid flows around a blunt body. Significant changes in the shock structure are observed, mainly due to special properties of the scheme in use and the influence of the domain transformation procedure. Perturbations in the supersonic flow upstream of the shock are also seen in the solution, which is a non-physical behavior. Freestream subtraction, flux limiting and the explicit addition of artificial dissipation are employed in order to circumvent these problems. One of the AUSM+ formulations presented here is seen to be particularly more robust in avoiding the appearance of some of these numerically-induced disturbances and non-physical characteristics in the solution. Good agreement is achieved with both numerical and experimental results available in the literature.}

physics.flu-dyn↗

arXiv2026

Numerical Aspects of Gradient Reconstruction Schemes Applied to Complex Geometries

This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different ways of formulating the limiter functions necessary to maintain stability in the presence of flow discontinuities. The flows of interest are simulated using the compressible Reynolds-averaged Navier-Stokes equations, and the negative Spalart-Allmaras model is used for turbulence closure. Definition of interface inviscid terms uses the Roe approximate Riemann solver, whereas the interface viscous terms are calculated with a standard centered scheme together with appropriate definitions of the interface gradients. Steady state solutions are obtained using an implicit time-integration method, together with a novel convergence acceleration technique. This new approach defines a set of three simple rules for controlling the global CFL number based on the residue evolution. The work considers three test cases, namely, the subsonic bump-in-channel flow, the subsonic NASA high-lift Common Research Model multielement airfoil and the transonic ONERA M6 wing. Present results are compared to experimental and numerical data available in the literature. Severe numerical instabilities are observed when the simplest gradient reconstruction technique is used, while more sophisticated formulations are able to provide excellent agreement with the existing literature. Current results are demonstrated to be highly insensitive to modifications made to the numerical flux entropy fix terms. Integrated aerodynamic forces are shown to be mildly dependent on the limiter formulation used, even in the absence of shock waves. The proposed convergence acceleration procedure manages to quickly drive the residue terms to machine zero, provided no major instabilities are present.

physics.flu-dyn↗

arXiv2023

Stability and Order of Accuracy Analysis of High-Order Schemes Formulated Using the Flux Reconstruction Approach

A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled with Runge-Kutta-type time-march procedures. Schemes are created using different numbers of internal points for each cell of the discrete domain, in such a way that a broad spectrum of spatial discretization orders can be analyzed. Multiple correction functions are employed so that well-known schemes, for instance the Discontinuous Galerkin (DG) and the Staggered-Grid schemes, may also be included in the study. The stability analysis is performed by identifying the behavior, in the complex plane, of the eigenvalues associated with each one of the considered cases. It is observed that, as the order of the scheme increases, a significant decrease in its domain of stability occurs, followed by a significant reduction in the amount of artificial dissipation that is introduced to the solution.

physics.flu-dyn↗

arXiv2023

On the Influence of Gradient Reconstruction Procedures Over the Accuracy of Finite Volume Based Schemes

In the context of the cell centered finite volume approach, care must be taken when performing the reconstruction of property gradients at cell interfaces. The present work analyzes three different gradient reconstruction procedures, using three different turbulent simulation test cases, namely the zero-gradient flat plate, the subsonic NACA 0012 airfoil and the transonic OAT15A airfoil. The analysis is concerned mainly with the usage of quadrilateral meshes. The gas dynamics equations are solved using an implicit implementation of Roe's second-order upwind scheme. The RANS closure problem is solved by using the negative Spalart-Allmaras turbulence model. The solution quality of each gradient discretization procedure is analyzed and compared to experimental data and other numerical solutions available in the literature. For the cases considered here, excellent agreement is obtained between the computed solutions and the expected results, regardless of which gradient reconstruction scheme is used.

physics.flu-dyn↗