Abstract An empirical mesh adaption algorithm is introduced for modeling one-dimensional reaction-diffusion systems with large moving gradients. Our new based on the revelation, that in high concentration gradients appear nearby to region where rate of reaction maximal, thus local can be used control adaption. We found, main advantage such a method its simplicity and easy implementation. As an ...

We propose an approach for structural optimization which combines the flexibility of the level set method for handling large deformations and topology changes with the accurate description of the geometry provided by an exact mesh of the shape. The key ingredients of our method are efficient algorithms for (i) moving a level set function on an unstructured mesh, (ii) remeshing the surface corre...

We consider a continuous formulation of moving mesh equations based on a relaxation of an equidistribution principle. Under natural assumptions on the monitor function, we derive bounds on the departure from equidistribution of the evolving mesh. Furthermore, we derive stability bounds for solutions of the equations based on the stability of the underlying PDE. Numerical examples are given to i...

We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in t...

A scheme using the mesh-free generalized finite differencing (GFD) on flows past moving bodies is proposed. The aim is to devise a method to simulate flow past an immersed moving body that avoids the intensive remeshing of the computational domain and minimizes data interpolation associated with the established computational fluid methodologies; as such procedures are time consuming and are a s...

in this paper, the effects of carbon nanotube (cnt) orientation and aggregation on the static behavior of functionally graded nanocomposite cylinders reinforced by cnts are investigated based on a mesh-free method. the used nanocomposites are made of the straight cnts that are embedded in an isotropic polymer as matrix. the straight cnts are oriented, randomly or aligned or local aggregated int...