N-body simulation program

Features

Integration methods

Method alias	Order	Description	Implicit	Dynamic step
adams	up to 5	Adams–Bashforth method	➖	➖
bs	2*max_level	Bulirsch-Stoer method	➖	⭐
euler	1	Classic Euler method	➖	➖
midpoint	2	Midpoint method	➖	➖
midpoint-st	2	Midpoint method (Stetter modification. See 1) p. 228)	⭐	➖
rk4	4	Classic Runge-Kutta 4-order method	➖	➖
rk_butcher	-	Runge-Kutta method with arbitrary Butcher tableu	➖	➖
rkck	5	Runge-Kutta-Cash–Karp 5-order method	➖	⭐
rkdp	5	Runge-Kutta-Dormand–Prince 5-order method	➖	⭐
rkdverk	5	Runge-Kutta-Verner 5-order method. See 1) p. 181	➖	⭐
rkf	7	Runge-Kutta-Fehlberg 7-order method. See 1) p. 180	➖	⭐
rkfeagin10	10	Runge-Kutta-Feagin 10-order method. See 4)	➖	⭐
rkfeagin12	12	Runge-Kutta-Feagin 12-order method.	➖	⭐
rkfeagin14	14	Runge-Kutta-Feagin 14-order method.	➖	⭐
rkgl	6	Gauss–Legendre 6-order method	⭐	➖
rklc	4	Runge-Kutta-Lobatto IIIC 4-order method	⭐	⭐
trapeze	2	Trapeze method	⭐	➖

Compute engines

Engine alias	Approximate	Description
ah	⭐	Single threaded engine with Ahmad-Cohen universe force simulation. See 2)
block	➖	Multi-threaded (OpenMP) engine with block-by-block force computation
cuda	➖	Parallel CUDA engine
cuda_bh	⭐	CUDA engine with Burnes-Hut force simulation
cuda_bh_tex	⭐	CUDA engine with Burnes-Hut force simulation and with bodies tree stored at texture memory. Possible tree layout is 'heap' and 'heap_stackless'
opencl	➖	Parallel OpenCL engine
opencl_bh	⭐	Parallel OpenCL engine with Burnes-Hut force simulation
openmp	➖	Multi-threaded (OpenMP) engine
simple	➖	Simple single threaded engine
simple_bh	⭐	Multi-threaded (OpenMP) engine with Burnes-Hut force simulation

How to run

Simulation

To run n-body problem simulation use 'nbody-simulation' programm.

Simulation control

Argument	Description
--stars_count	Stars count
--box_size	'Universe' box size.
--output	Output stream name.
--resume	Stream name to resume (in this case output and initial_state are ignored).
--initial_state	Optional initial state file
--initial_type	Initial state type. Possible values are: Zeno, G1, SI, ADK. See initial state types table.
--max_part_size	Max stream file size (splits a stream into multiple files).
--max_time	Max simulation time.
--dump_step	Time step to dump simulation state to stream.
--check_step	Time step to verify the fundamental laws of physics. Conservation of impulse [P], angular momentum [L], energy [E], mass center velocity [V].
--check_list	List of fundamental laws of physics to check. For example --check_list=PL to check only conservation of impulse [P] and angular momentum [L].
--verbose	Print detailed simulation information.

Initial state types

Type	Description
Zeno	File in 'Zeno' format. Can be created with snapascii tool.
G1	Plane text table with Rx Ry Rz Vx Vy Vz M values. Space as separator.
SI	Plane text table same format as G1. Units are meter, second, kilogram. On load mass will be multiplied by MassFactorSI to convert to G1 type.
ADK	Plane text table same format as G1. Units are astronomical unit, day, kilogram. On load mass will be multiplied by MassFactorAuDayKg to convert to G1 type.

Engine control arguments are:

Argument	Description
--engine	Compute engine type.
--distance_to_node_radius_ratio	Simulation accuracy control for Burnes-Hut engines.
--traverse_type	Space tree traverse type for Burnes-Hut engine. Possible values are cycle or nested_tree.
--tree_layout	Space tree layout type for Burnes-Hut engine. Possible values are tree or heap.
--full_recompute_rate	Full force recompute rate in cucles (Ahmad-Cohen engine).
--max_dist	The maximum distance at which the force is calculated completely at each step (Ahmad-Cohen engine).
--min_force	The minimum force of attraction at which it is calculated completely at each step (Ahmad-Cohen engine).
--device	Platforms/devices list for OpenCL based engines. Format: Platform1_ID:Device1,Device2;Platform2_ID:Device1,Device2... For example: --device=0:0,1 - first and second devices from first platform (with same context), --device=0:0;0:1 - first and second devices from first platform (with separate contexts)
--oclprof	Enable OpenCL profile
--block_size	Data block size to load at local OpenCL/CUDA memory

Solver control arguments are:

Argument	Description
--solver	Solver type.
--max_step	Solvers max time step
--min_step	Embedded solvers min time step
--rank	Adams–Bashforth solver rank (1...5).
--correction	Kahan summation at each integration step (for now at Adams–Bashforth and Runge-Kutta solvers)
--starter_solver	Adams–Bashforth starter solver.
--refine_steps_count	Refine step count for implicit solvers.
--error_threshold	Step error threshold for solvers with dynamic step. If the error at the current step is greater than the threshold, then we decrease the time step and repeat the step.
--max_recursion	Max recursion level for embeded solvers.
--substep_subdivisions	Number of embeded solver substeps into which the current step is divided at the next level of recursion when the error greater than error_threshold.
--max_level	Maximum extrapolation table size for Bulirsch-Stoer solver

Player

To view simulation results run 'nbody-player' programm.

Argument	Description
--input	Input stream name.
--check_list	List of fundamental laws of physics to check. For example --check_list=PL to check only conservation of impulse [P] and angular momentum [L].

Other parameters controlled via UI.

Gallery

Refs

1. Hairer, Ernst; Nørsett, Syvert Paul; Wanner, Gerhard (1993), Solving ordinary differential equations I: Nonstiff problems, Berlin, New York
2. A Numerical Integration Scheme for the N-Body Gravitational Problem A. AHMAD AND L. COHEN 1973
3. Задача N тел или как взорвать галактику не выходя из кухни
4. Feagin T. A tenth-order Runge–Kutta method with error estimate. In: Proc. of the IAENG Conf. on Scientific Computing. Hong Kong, 2007.