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The impetus of this research is to present a generalized Bernoulli Trial collision scheme in the context of the direct simulation Monte Carlo (DSMC) method. Previously, a subsequent of several collision schemes have been put forward, which were mathematically based on the Kac stochastic model. These include Bernoulli Trial (BT), Ballot Box (BB), Simplified Bernoulli Trial (SBT) and Intelligent Simplified Bernoulli Trial (ISBT) schemes. The number of considered pairs for a possible collision in the above-mentioned schemes varies between N ( l ) ( N ( l ) − 1 ) / 2 in BT, 1 in BB, and ( N ( l ) − 1 ) in SBT or ISBT, where N ( l ) is the instantaneous number of particles in the l th cell. Here, we derive a generalized form of the Bernoulli Trial collision scheme (GBT) where the number of selected pairs is any desired value smaller than ( N ( l ) − 1 ), i.e., N sel < ( N ( l ) − 1 ) , keeping the same the collision frequency and accuracy of the solution as the original SBT and BT models. We derive two distinct formulas for the GBT scheme, where both formula recover BB and SBT limits if N sel is set as 1 and N ( l ) − 1 , respectively, and provide accurate solutions for a wide set of test cases. The present generalization further improves the computational efficiency of the BT-based collision models compared to the standard no time counter (NTC) and nearest neighbor (NN) collision models. [ABSTRACT FROM AUTHOR]

The current paper examines a new DSMC approach to hypersonic flow simulation consisting of a combination between the Simplified Bernoulli Trials (SBT) collision algorithm and the transient adaptive subcell (TAS) selection procedure. The SBT collision algorithm has already been introduced as a scheme that provides accurate results with a quite small number of particles per cells and its combination with the transient adaptive subcell (TAS) technique will enable SBT to have coarser grid sizes as well. In the current research, the no-time-counter (NTC) collision algorithm and nearest neighbor (NN) pair selection procedure of Bird DS2V code are substituted by the SBT-TAS and comparisons between the new algorithm and NTC-NN are made considering appropriate test cases including hypersonic cylinder flow and axisymmetric biconic flow. Hypersonic cylinder flow is a well-known benchmark problem with a wide collision frequency range while the biconic flow exhibits laminar shock/shock and shock/boundary-layer interactions. Improvements implemented in the SBT-TAS technique, including subcell volume estimation, surface properties filter, and time controller, are discussed in detail. The simulations of these hypersonic test cases demonstrated that from the viewpoint of consumed sample-size, SBT-TAS is an efficient collision technique. [ABSTRACT FROM AUTHOR]