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Ebrahim Nabizadeh
Department of Mechanical Engineering, Rice University, Houston, Texas 77005, USA

Darrell W. Pepper
NCACM, Department of Mechanical Engineering, University of Nevada Las Vegas, Las Vegas, NV 89154, USA

DOI: 10.1615/TFEC2017.asp.017999
pages 101-105


A shock wave is a form of a propagating disturbance. Like an ordinary wave, a shock carries energy and can propagate through a medium. One of the major difficulties in computational fluid dynamics (CFD) is the generation of suitable meshes for this type of flow. A proper mesh can require considerable effort to generate for a compressible flow problem involving complex configurations. In order to reduce the high cost of mesh generation, various numerical schemes have been proposed. Among them, the relatively recent meshless method employs a very simple technique to generate node points within the problem domain. Existing conventional computational techniques require a mesh to discretize the domain and yield solutions. However, the accuracy of the numerical approach depends upon the quality of the mesh. In this study, a localized meshless method employing multiquadrics (MQs) radial basis functions (RBFs) [1] is used to approximate the terms within the governing equations. The concern of an ill-conditioned matrix, as well as the computational burden of having to evaluate several large matrices, is mitigated by using a localized meshless approach [2].
The localized RBF-MQ technique is used to develop a meshfree Euler solver for inviscid compressible flow. The issue in solving hyperbolic PDEs such as Euler equations is to use a suitable discretization method, which not only can accurately approximate the smooth regions of flow but also have the ability of capturing the discontinuities, or shocks, within the flow field [3]. In the present scheme, a hybrid upwind technique is used to accurately resolve the shock location and propagation.

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