Accumulators
Often the quantity of interest in particle tracing simulations involves the interaction of particles with fields defined on a set of domains or boundaries. Examples of particle-domain interactions include the accumulation of space charge density due to ions and electrons, and the volume force exerted by moving particles on the surrounding fluid. Examples of notable particle-boundary interactions include erosion due to the impact of solid particles on a surface, sputtering of surface molecules due to the impact of ions at a high velocity, and boundary loads generated by a stream of particles impinging on a surface.
An Accumulator is a physics feature that allows dependent variables that are defined on domain or boundary mesh elements to be affected by particles that interact with those elements. When an Accumulator is added directly to a physics interface, it defines a variable, called an accumulated variable, in each mesh element in a set of domains. The value of the accumulated variable in a mesh element is affected by the presence of particles within that element. Particles may either affect the accumulated variable directly, by changing the value of the accumulated variable within the mesh element occupied by the particle; or by changing the accumulated variable’s time derivative.
When an Accumulator is added as a subnode to a Wall, Outlet, or Axial Symmetry node, it defines an accumulated variable on boundary elements in the selection list of its parent node, defining one degree of freedom per element. These degrees of freedom are incremented as particles hit the boundary. For more information on the Accumulator features, see Accumulator (Boundary) and Accumulator (Domain).
The Accumulator features are available with all particle tracing interfaces. In addition, the following features are available in The Charged Particle Tracing Interface to define accumulated variables for more specialized applications: Etch, Surface Charge Density, Current Density, and Heat Source.
The following features in The Particle Tracing for Fluid Flow Interface define accumulated variables for specific applications: Erosion, Mass Deposition, Boundary Load, and Mass Flux.
The dedicated Multiphysics nodes and interfaces described in the section Multiphysics Couplings also use special cases of accumulators on domains to model particle-field and fluid-particle interactions.
Because each particle’s location is defined as a point whereas the accumulated variables are defined on mesh elements of finite size, accumulators are inherently mesh dependent. If the accumulated variable is the density of a physical quantity, it tends to become infinitely large in the limit as the mesh elements become infinitesimally small. To obtain reasonable solutions, the number of particles moving through a domain or interacting with the boundary should typically be at least an order of magnitude larger than the total number of domain elements in a typical cross section of the domain or the total number of elements on the boundary, respectively.