Non-orthogonal transformation of irregular geometry for particle based simulation

Simulations of irregular geometries using non-orthogonal transformation is widely used in grid based methodology such as computational fluid dynamics. However, this approach is not utilized for particle based models. In this paper we introduce non-orthogonal transformation to simulate fluid flow in irregular geometry using dissipative particle dynamics (DPD). Applying boundary condition is not trivial in DPD methodology and problem becomes more complicated for irregular boundary. In the present work, irregular (physical) domain is transformed into a rectangular domain and boundary particles are frozen along the wall. Transformation for position and velocity is used to relate physical and computational domains. As particle's position and velocity change with time, transformation matrices are determined for each DPD particle at every time step. In DPD, forces are function of actual distance between the particles and acts within a cutoff radius, which change in transformed domain at every location. To solve this problem, firstly, interacting particles are identified in the physical domain and then forces are calculated in the transformed domain. This approach is described by simulating fluid flow inside a convergent-divergent nozzle, whose geometry is controlled by the contraction ratio (CR) in the middle of the nozzle. The DPD results were validated against in-house computational fluid dynamic (CFD) finite volume code based on the stream function vorticity approach. The range of Reynolds number and CR, under study here, is Re = 10 - 200 and CR=0.8 and 0.6, respectively. The results revealed an excellent agreement between the DPD and CFD. The maximum deviation between the DPD and CFD results is within 2%. It is found that using large values of dissipative force parameter velocity fluctuations are less. Keywords: Dissipative particle dynamics, DPD, nonorthogonal transformation, grid generation, Irregular geometry, nozzle.