Model of Groundwater Flow Using Boltzmann Lattice-Gas Automation Method In Maros Karst Region, Indonesia

In this study, modeling of mineral resources of underground water in karst mountain area of Maros-Pangkep, Indonesia was made by the Boltzmann lattice-gas automata method. This method was applied to solve the problem of groundwater flow by viewing them as a lattice gas. Simulation models of groundwater flow in the form of 16 and 32 particle size with a barrier particles form a circle on the plate and different variations of time to reach steady its state. The simulation 10 results showed that the greater the time duration, the more different fluid motion pattern. For the state of the karst region, this means that the heterogeneous medium karst very unstable and affect the movement of the particles. In addition, karstification process takes place in a relatively long time with adequate rainfall.

2 Lattice gas automata method can be used for several different types of mixed fluid flow characteristics or fluid through the medium of complex geometry structure (Arsyad, 1999;Supriyatno, 1998). Model-lattice Boltzmann gas consists of particles that move from one cell to another in a triangular lattice (Rothman, 1990).
Simulations will be made showed that the hydrodynamic flow pattern with particles or molecular dynamics simulations (Aharonof and Rothman, 1993;Rothman, 1988). Such modeling was applied to solve fluid flow problems by viewing them 5 as lattice-gas (Khotimah and Liong, 2002), especially for heterogeneous medium with complex boundaries, such as medium karst region.

Research Method
Location of sampling research conducted in Maros, located between 40°45'50" LS and 109°20'00'' lon.E up with 129°12'00'' lon.E. Furthermore, made simulations to model groundwater flow patterns using computer of 2930 Intel Aspire computer, 10 Intel ® Core TM Duo processor T6400 (2.0 Ghz, 800 MHz FSB, 2 MB L2 cache), Mobile Intel ® Graphics Media Accelerator 4500 MHD, 1 GB DDR2, 12.1" WXGA Acer CrystalBrite TM LCD, 250 GB HDD, DVD-Super Multi DL, dan 802.11 The data required to perform the simulation model of groundwater flow in karst region are the physical properties of the medium Maros karst region that includes, coefficient of permeability, porosity and density of the medium as shown in Table  15 1.
This study uses the time t and t + n as the data to simulate fluid flow, so that: 1. Data on the physical properties of the medium are constant, the porosity (), soil particle density (), and the permeability of the medium () as in the table 1.
2. Simulation with Lattice-Gas is the model used to facilitate molecular movement known as the Lattice-Gas Automata. 20 Model Lattice-Gas Boltzmann consists of particles that move from one cell to another in a triangular lattice. Using the lattice equilateral triangle of each particle can have six possible directions speed. Each particle have a mass unit and one unit of speed. The total momentum of the collision is zero and the particle rotated 60 degrees. Because the particles in the Gas-Lattice Boltzmann be described as a boolean variable   t x n i , , with the direction determined by the speed unit (Wolf-Gladrow, 2000): 25 (1) so that the particle moves by following a mathematical equation and is written: is the collision operator that describes changes in the value n i (x, t). These collisions can be valuable operator 0, +1, or -1. If there is no change in the number of particles in the direction i caused by collision events, ie the number of particles before and after the collision in the direction i are same, then the value of       The price in Table 1, further processed to obtain the movement of ground water medium in Maros karst region, the algorithm as follows 1) Input parameters of time duration flow by N units of time.
2) create a medium with properties of the medium as in Table 1 .  10 3) placing the initial position of particles in a triangular lattice such that the total momentum of the collision is zero and the particles allows rotated 60 degrees (Rothman, 1988). 4) Particles in the Boltzmann lattice gas can be described as a boolean variable n i (x,t), the direction is determined by the speed unit of 2 sin 6 2 cos 15 with i = 1, 2, …. 6. 5) Particle motion, every one unit of time, the particles move in the direction of the lattice unit speed. 6) Tracking was done at each lattice configuration to determine whether there was the possibility of change in the direction of the particles caused by the collision with a wall or occurs whether or not the configuration, so that : a) if there was a change in the direction of the particle or configuration changes, then the transformation was done on the basis of the 20 data, and b ) if no change in the direction of the particle or configuration changes, then the program straight to step 6 7) Repeat steps (1) to (5) was performed until the time parameter achieve N as unit time given input. 8) Display the results 9) Finish. 25 The simulation began with the movement of fluid due to the difference in pressure on both the left and right sides. Fluid moves until it reaches equilibrium. Equilibrium occurs if the time is still moving, but the flow has shown a similar pattern.
That is, the time is growing but the flow pattern remains the same. So the simulation stopped if the flow pattern does not change anymore. In this study, it doing extraction/pumping out of water. The movement of groundwater in medium karst areas is very different with medium nonkarst. The heterogeneous of medium characteristic effect on fluid motion. Continuously of fluid motion obtain changes of pressure gradient will cause the process of kartisification be slow. Karstification will determine the characteristic of constantly changing of medium in proportion to time. If the pattern of flow shown in this simulation is not changed, then karstification started, thus permeable of medium karst becomes impermeable, so that the medium be a water 5 reservoir that holds water in a relatively long time. This process will lead to the karst region has uvala, polje and karst characteristics as water tendon is different from other nonkarst medium. And Selection of a barrier in the form of plate adapted to the characteristic of medium karst is vertical barrier wall. Dimensions of plate depending on the size of the Lattice Boltzmann that allows particles to move with 6 possible directions as equation (1).
For barriers of circle adapted to the characteristic of medium karst that has undergone karstification. Karstification occur if 10 the medium that was rigid and stiff, because dissolution occurs deformation. This deformation caused barrier fluid movement turns into a circle particles with dimensions larger than the dimensions of the particles that started from 16, 32, etc.

Result and Discussion
Simulation models of groundwater flow in Maros karst region were divided into two major parts of the groundwater flow 15  Drink. Water Eng. Sci. Discuss., doi:10.5194/dwes-2016-9, 2017 Drinking Water  The simulation results indicated that the karstification process takes place in a relatively long time with adequate rainfall.
Therefore, the situation is very dependent on the state of the micro-climate of the region, especially the state of rainfall.
Rainfall is one of elements of the climate which is associated with the other elements of the climate, such as the ambient temperature and humidity. Study conducted by (Ahmad and Hashim, 2010) (Sanusi et al., 2015) showed that a change in one element of the climate will affect the other climatic elements, such as the air temperature increases followed by increased 15 rainfall. Furthermore, the high temperatures in the area where the water is in short supply, will lead to an increase in air humidity. If this situation occurs in-Pangkep Maros karst region, it will certainly affect the karstification in the region. In addition, this process is also affected by karst topography are available and endogenous processes in karst itself. The result was a cycle of water in karst areas more not follow the water cycle.
Water collected in the karst hills on epikarst zone is slowly through the slits vadose, fracture, and then fill the underground 20 stream that continues to evolve into an underground river. Therefore, springs or underground rivers in Maros Karst Region will have a time delay after rain events for a few moments with the chemical quality of water is relatively good.

Conclusion
Mineral resource modeling of groundwater in karst mountain area of Maros-Pangkep had been conducted using the Boltzmann lattice gas automata. The result was a simulation of the hydrodynamic flow patterns by viewing them as lattice 25 gas. The simulation results showed that the greater the time duration, the more different fluid motion pattern. For the state of the karst region, this means that the heterogeneous medium karst very unstable and affect the movement of the particles. In addition, karstification process takes place in a relatively long time with adequate rainfall. This process is not only dependent on karst topography are available, but also on endogenous processes in karst itself.