The stability and accuracy of the Generalized Interpolation Material Point (GIMP) Method is measured directly through carefully-formulated manufactured solutions over wide ranges of CFL numbers and mesh sizes. The manufactured solutions are described in detail. The accuracy and stability of several time integration schemes are compared via numerical experiments. The effect of various treatment of particle "size" are also considered. The hypothesis that GIMP is most accurate when particles remain contiguous and non-overlapping is confirmed by comparing manufactured solutions with and without this property.

This paper presents the results of an experimental study of forced convection heat transfer in a narrow rectangular duct fitted with an elliptical tube and one or two delta-winglet pairs. The duct was designed to simulate a single passage in a fin-tube heat exchanger. Heat transfer measurements were obtained using a transient technique in which a heated airflow is suddenly introduced to the test section. High-resolution local fin-surface temperature distributions were obtained at several times after initiation of the transient using an imaging infrared camera. Corresponding local fin-surface heat transfer coefficients were then calculated from a locally applied one-dimensional semi-infinite inverse heat conduction model. Heat transfer results were obtained over a Reynolds number range based on duct height of 670–6300. Pressure-drop measurements have also been obtained for similar elliptical-tube and winglet geometries, using a separate single-channel, multiple-tube-row pressure-drop apparatus. The pressure-drop apparatus includes four tube rows in a staggered array. Comparisons of heat transfer and pressure-drop results for the elliptical tube versus a circular tube with and without winglets are provided. Mean heat transfer results indicated that the addition of the single winglet pair to the oval-tube geometry yielded significant heat transfer enhancement, averaging 38% higher than the oval-tube, no-winglet case. The corresponding increase in friction factor associated with the addition of the single winglet pair to the oval-tube geometry was very modest, less than 10% at ReDh=500 and less than 5% at ReDh=5000.

SUMMARYA novel meshfree method is proposed that incorporates features of the material point (MPM) and generalized interpolation material point (GIMP) methods and can be used within an existing MPM/GIMP implementation. Weighted least squares kernel functions are centered at stationary grid nodes and used to approximate field values and gradients. Integration is performed over cells of the background grid and material boundaries are approximated with an implicit surface. The proposed method avoids nearest-neighbor searches while significantly improving accuracy over MPM and GIMP. Implementation is discussed in detail and several example problems are solved, including one manufactured solution which allows measurement of dynamic, non-linear, large deformation performance. Advantages and disadvantages of the method are discussed.

SUMMARYThe material-point method models continua by following a set of unconnected material points throughout the deformation of a body. This set of points provides a Lagrangian description of the material and geometry. Information from the material points is projected onto a background grid where equations of motion are solved. The grid solution is then used to update the material points. This paper describes how to use this method to solve quasi-static problems. The resulting discrete equations are a coupled set of nonlinear equations that are then solved with a Jacobian-free, Newton-Krylov algorithm. The technique is illustrated by examining two problems. The first problem simulates a compact tension test and includes a model of material failure. The second problem computes effective, macroscopic properties of a polycrystalline thin film.