Dynamic Unstructured Mesh Optimization for Improved Modelling of Flow and Transport in Highly Heterogeneous Aquifers

Monday, October 5, 2015
Matthew Jackson, Pablo Salinas, James R Percival, Dimitrios Pavlidis, Christopher Pain, Hossam Osman, Alexander Adam, Carl Jacquemyn, Gerard Gorman and Gary Hampson, Imperial College London, London, United Kingdom
Abstract:
In most approaches to modelling flow in porous media, the grid is defined early in the modelling process and remains fixed irrespective of the numerical solution required. However, in many problems, especially those involving flow and transport in highly heterogenous porous media, higher grid resolution is required in specific regions of the model where gradients in a property of interest (e.g. head, concentration) are large, and lower resolution is acceptable elsewhere. For example, high resolution may be required in models of complex aquifers to resolve the location of the water table, especially close to abstraction boreholes, but lower resolution elsewhere may yield the same quality of solution for a given metric (such as local drawdown). We describe here a new approach to modelling flow and transport in heterogenous porous media, in which computational resources are used more efficiently by adapting an unstructured mesh in space and time to be optimal for the numerical solution of interest. The new approach is facilitated by the use of

  1. A surface-based representation of geologic heterogeneity, constructed prior to the definition of any grid or mesh

  2. Unstructured tetrahedral meshes to discretize the rock volumes defined by the surfaces, and a dynamic adaptive mesh optimization (AMO) algorithm that optimizes the mesh for the required numerical solution

  3. A Control-Volume-Finite-Element-Method (CV-FEM) to solve the governing flow equations that is integrated with the AMO algorithm

The new modelling approach allows dynamic AMO to be applied in complex porous media without requiring the material properties to be up-, cross- or downscaled each time the mesh is optimized, or calculated a-priori in a pre-processing step. Geologic heterogeneity, that controls the spatial variation in material properties, is represented using surfaces constructed without reference to a grid or mesh defined early in the modelling process. When numerical solutions are required, an unstructured tetrahedral mesh is created that preserves the complex surface architecture. The local resolution of the mesh can be optimized in between the time-steps of a numerical simulation when required. The approach allows better representation of complex heterogeneity, flow and transport at lower computational cost.

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