arXiv subjects

Kun Qu

Publications and source records attributed to Kun Qu.

4 recordsLinked to original sources

arXiv2022

Finite volume based film flow and ice accretion models on aircraft wings

The thin runback water films driven by the gas flow, the pressure gradient and the gravity on the iced aircraft surface are investigated in this paper. A three-dimensional film flow model based on Finite Volume Method (FVM) and the lubrication theory is proposed to describe the flow. The depth-averaged velocity of the film is stored in Cartesian coordinates to avoid the appearance of the metric tensors. The governing equations are discretized in the first layer structured grid cell which is selected as the grids for film flow. In order to verify this method, comparisons between numerical results and experimental results of ice shapes on NACA 0012 airfoil and GLC-305 swept wing are presented, both showing a good agreement for rime and glaze ice condition. Overall, this model shows great potential to model ice accretion reasonably under different icing conditions. Besides, the present method doesn't require analytic metric terms, and can be easily coupled to existing finite volume solvers for logically Cartesian meshes.

physics.flu-dyn↗

arXiv2021

High Order Hermite Finite Difference Method for Euler/Navier-Stokes Equations in 2D Unstructured Meshes

A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each vertex is computed directly from fluxes nearby by means of high order least-square. In order to capture discontinuities, numerical flux of high order accuracy is calculated on each edge and serves as supporting data of the least-square computation of the divergence. The high accuracy of the numerical flux depends on the high order WENO interpolation on each edge. To reduce the computing cost and complexity, a curvlinear stencil is assembled for each edge so that the economical one-dimensional WENO interpolation can be applied. With the derivatives introduced, two-dimensional Hermite interpolation on a curvilinear stencil is applied to keep the stencil compact and avoids using many supporting points. In smooth region, the Hermite least-square 2D interpolation of 5 nodes is adopted directly to achieve the fifth order accuracy. Near a discontinuity, three values obtained by means of least-square 2D interpolation of 3 nodes, are weighted to obtain one value of the second order accuracy. After obtaining the flow states on both sides of the middle point of an edge, numerical flux of high order accuracy along the edge can be calculated. For inviscid flux, analytical flux on vertices and numerical flux along edges are used to compute the divergence. While for viscous flux, only analytical viscous flux on vertices are used. The divergence of the fluxes and their derivatives on each vertex are used to update the conservative variables and their derivatives with an explicit Runger-Kutta time scheme. Several canonical numerical cases were solved to test the accuracy and the capability of shock capturing of this method.

math.NA↗

arXiv2021

A Novel Finite Difference Method for Euler Equations in 2D Unstructured Meshes

Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this step, a one-dimensional curvilinear stencil is assembled for each edge to perform one-dimensional fast non-uniform WENO interpolation derived in this paper, which is much easier and faster than multi-dimensional interpolation. The second step is to compute the divergence of fluxes at each vertex from the fluxes at nearby edges and vertices by least square approximation of multi-dimensional polynomials. The order of the WENO interpolation in the first step and the degree of the polynomial in the second step determined the order of accuracy of the spatial scheme. After that, explicit RungeKutta time discrete scheme is used to update conservative variables. Several canonical numerical cases were solved to test the accuracy, performance and the capability of shock capturing of the developed method.

physics.comp-ph↗

arXiv2020

A sufficient condition for free-stream preserving in the nonlinear conservative finite difference schemes on curvilinear grids

In simulations of compressible flows, the conservative finite difference method (FDM) based on the nonlinear upwind schemes, e.g. WENO5, might violate free-stream preserving (FP), due to the loss of the geometric conservation law (GCL) identity when applied on the curvilinear grids. Although some techniques on FP have been proposed previously, no general rule is given for this issue. In this paper, by rearranging the upwind dissipation of the nonlinear schemes as a combination of sub-stencil reconstructions (taking WENO5 as an example), it can be proved that the upwind dissipation diminishes under the uniform flow condition if the metrics yield an identical value under the same schemes with these reconstructions, making the free-stream condition be preserved. According to this sufficient condition, the novel FP metrics are constructed for WENO5 and WENO7. By this means the original forms of these WENO schemes can be kept. In addition, the accuracy of these schemes can be retained as well with a simple accuracy compensation by replacing the central part fluxes with a high-order one. Various validations indicate that the present FP schemes retain the great capability to resolve the smooth regions accurately and capture the discontinuities robustly.

physics.comp-ph↗