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It is well known that there are two integral steps of streaming and collision in the lattice Boltzmann method (LBM). This concept has been changed by the author's recently proposed macroscopic lattice Boltzmann method (MacLAB) to solve the Navier-Stokes equations for fluid flows. The MacLAB contains streaming step only and relies on one fundamental parameter of lattice size dx, which leads to a revolutionary and precise minimal "Lattice" Boltzmann method, where physical variables such as velocity and density can be retained as boundary conditions with less required storage for more accurate and efficient simulations in modelling flows using boundary condition such as Dirichlet's one. Here, the idea for the MacLAB is further developed for solving the shallow water flow equations (MacLABSWE). This new model has all the advantages of the conventional LBM but without calculation of the particle distribution functions for determination of velocity and depth, e.g., the most efficient bounce-back scheme for no-slip boundary condition can be implemented in the similar way to the standard LBM. The model is applied to simulate a 1D unsteady tidal flow, a 2D wind-driven flow in a dish-shaped lake and a 2D complex flow over a bump. The results are compared with available analytical solutions and other numerical studies, demonstrating the potential and accuracy of the model.

The birth of the lattice Boltzmann method (LBM) fulfils a dream that simple arithmetic calculations can simulate complex fluid flows without solving complicated partial differential flow equations. Its power and potential of resolving more and more challenging physical problems have been and are being demonstrated in science and engineering covering a wide range of disciplines such as physics, chemistry, biology, material science and image analysis. The method is a highly simplified model for fluid flows using a few limited fictitious particles that move one grid at a constant time interval and collide each other at a grid point on uniform lattices, which are the two routine steps for implementation of the method to simulate fluid flows. As such, a real complex particle dynamics is approximated as a regular particle model using three parameters of lattice size, particle speed and collision operator. A fundamental question is "Are the two steps integral to the method or can the three parameters be reduced to one for a minimal lattice Boltzmann method?". Here, I show that the collision step can be removed and the standard LBM can be reformulated into a simple macroscopic lattice Boltzmann method (MacLAB). This model relies on macroscopic physical variables only and is completely defined by one basic parameter of lattice size dx, bringing the LBM into a precise "Lattice" Boltzmann method. The viscous effect on flows is naturally embedded through the particle speed, making it an ideal automatic simulator for fluid flows. The findings have been demonstrated and confirmed with numerical tests including flows that are independent of and dependent on fluid viscosity, 2D and 3D cavity flows, and an unsteady Taylor-Green vortex flow. This provides an efficient and powerful model for resolving physical problems in various disciplines of science and engineering.

In this paper, we seek an adequate macroscopic model for a hydraulic jump in Bingham fluid. The formulas for conjugate depths, sequent bottom shear stress and critical depth are established. Since no exact analytical solution in closed form is available for conjugate depths, an approximate formula is developed. This formula can provide good results with an error less than 4%. The analytical results have revealed that the critical depth and the ratio of conjugate depths increase until bottom shear stress exceeds a certain value and then decrease afterwards. The bottom shear stress downstream of the jump is smaller than that upstream. The results are verified by experimental data and observations available in the literature.

The forward-backward multiplicity and correlations of target evaporated fragment(black track particle) and target recoiled proton(grey track particle) emitted in 150 A MeV He-emulsion, 290 A MeV C-emulsion, 400 A MeV C-emulsion, 400 A MeV Ne-emulsion and 500 A MeV Fe-emulsion interactions are investigated. It is found that the forward and backward averaged multiplicity of grey, black and heavily ionized track particle increase with the increase of target size. Averaged multiplicity of forward black track particle, backward black track particle, and backward grey track particle do not depend on the projectile size and energy, but the averaged multiplicity of forward grey track particle increases with increase of projectile size and energy. The backward grey track particle multiplicity distribution follows an exponential decay law and the decay constant decreases with increase of target size. The backward-forward multiplicity correlations follow linear law which is independent of the projectile size and energy, and the saturation effect is observed in some heavy target data sets., Comment: 18 pages, 8 figures