Xia Ma

Material point method enhanced by modified gradient of shape function

A numerical scheme of computing quantities involving gradients of shape functions is introduced for the material point method (MPM), so that the quantities are continuous as material points move across cell boundaries. The noise and instability caused by cell crossing of the material points are then eliminated. In this scheme, the formulas used to compute these quantities can be expressed in the same forms as in the original material point method, but with the gradient of the shape function modified. For one-dimensional cases, the gradient of the shape function used in the generalized interpolation material point (GIMP) method is a special case of the modified gradient if the characteristic function of a material point is introduced. The characteristic function of a material point is not otherwise needed in this scheme, therefore difficulties in tracking its evolution are avoided. Although the support of the modified gradient of a shape function is enlarged from the cell containing the material point to also include the immediate neighbor cells, all the non-local effects of a material point can be accounted for by two consecutive local operations. Therefore this scheme can be used in calculations with unstructured grids. This scheme is proved to satisfy mass and momentum conservations exactly. The error in energy conservation is shown to be second order on both spatial and temporal discretizations. Although the error in energy conservation is the same order as that in the original material point method, numerical examples show that this scheme has significantly better energy conservation properties than those of the original material point method.

Material point method applied to multiphase flows

The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. Its application to multiphase flows or multi-material deformations, however, encounters a numerical difficulty of satisfying continuity requirement due to the inconsistence of the interpolation schemes used for different phases. It is shown in Section 3 that current methods of enforcing this requirement either leads to erroneous results or can cause significant accumulation of errors. In the present paper, a different numerical method is introduced to ensure that the continuity requirement is satisfied with an error consistent with the discretization error and will not grow beyond that during the time advancement in the calculation. This method is independent of physical models. Its numerical implementation is quite similar to the common method used in Eulerian calculations of multiphase flows. Examples calculated using this method are presented.

Centrifugal Contactors: Separation of an Aqueous and an Organic Stream in the Rotor Zone (LA‐UR‐05‐7800)

Abstract A multi‐phase flow code is used to simulate the separation of an aqueous and an organic stream in the rotor zone of an annular centrifugal contactor. Different values for the mixture viscosity and for the initial volume fractions of the components are considered. A simple model for mass transfer of a species between phases is used. Geometrical effects are found to have significant influence on the separation of the two‐phase mixture.

Distribution coefficient algorithm for small mass nodes in material point method

When using the time explicit material point method to simulate interaction of materials accompanied by large deformations and fragmentation, one often encounters a numerical instability caused by small node mass, because acceleration on a mesh node is obtained by dividing the total force on the node by the mass of the node. When the material points are in the far sides of the cells containing the node, typically happening near material interfaces, the node mass can be very small leading to artificially large acceleration and then numerical instability. For the case of small material deformations, this instability is typically avoided by placing the material points away from cell boundaries. For cases with large deformations, with the exception of initial conditions, there is no control on locations of the material points. The instability caused by small mass nodes is often encountered. To avoid this instability tiny time steps are usually required in a numerical calculation. In this work, we present a numerical algorithm to treat this instability. We show that this algorithm satisfies mass and momentum conservation laws. The error in energy conservation is proportional to the second order of the time step, consistent with the explicit material point method. Numerical implementation of the algorithm is described. Numerical examples show effectiveness of the algorithm.

A Separate-Phase Drag Model and a Surrogate Approximation for Simulation of the Steam-Assisted-Gravity-Drainage Process

General ensemble phase averaged equations for multiphase flows have been specialized for the simulation of the steam assisted gravity drainage (SAGD) process. In the average momentum equation, fluid-solid and fluid-fluid viscous interactions are represented by separate force terms. This equation has a form similar to that of Darcy’s law for multiphase flow but augmented by the fluid-fluid viscous forces. Models for these fluid-fluid interactions are suggested and implemented into the numerical code CartaBlanca. Numerical results indicate that the model captures the main features of the multiphase flow in the SAGD process, but the detailed features, such as plumes are missed. We find that viscous coupling among the fluid phases is important. Advection time scales for the different fluids differ by several orders of magnitude because of vast viscosity differences. Numerically resolving all of these time scales is time consuming. To address this problem, we introduce a steam surrogate approximation to increase the steam advection time scale, while keeping the mass and energy fluxes well approximated. This approximation leads to about a 40-fold speed-up in execution speed of the numerical calculations at the cost of a few percent error in the relevant quantities.

NSR&D FY14 Final Report: Friction/Impact Modeling

The LANL-developed CartaBlanca code uses advanced techniques, including the Dual Domain Material Point (DDMP) method, to calculate fluid, solid motions and fluid-structure interactions. In the last year we have implemented the ViscoSCRAM material model in CartaBlanca based on Clements’ Abaqus-Explicit Finite Element implementation. In this fiscal year, we study numerical properties of this implementation. To consider coupled mechanical, thermal and chemical effects, we have implemented Henson’s HE decomposition model to couple with the thermal and mechanical packages in CartaBlanca. We have also developed porous media flow modules to consider heat convection effects of the reaction product gas inside pores of HE. The next immediate step is to perform numerical simulations to study interactions among these different mechanisms. We have started such calculation and obtained interesting initial results at the end of this fiscal year.