deeplearning/modulus/modulus-sym-v130/_modules/modulus/sym/eq/pdes/turbulence_zero_eq.html

Source code for modulus.sym.eq.pdes.turbulence_zero_eq

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"""Zero Equation Turbulence model
References:
https://www.eureka.im/954.html
https://knowledge.autodesk.com/support/cfd/learn-explore/caas/CloudHelp/cloudhelp/2019/ENU/SimCFD-Learning/files/GUID-BBA4E008-8346-465B-9FD3-D193CF108AF0-htm.html
"""

from sympy import Symbol, Function, sqrt, Number, Min

from modulus.sym.eq.pde import PDE


[docs]class ZeroEquation(PDE): """ Zero Equation Turbulence model Parameters ========== nu : float The kinematic viscosity of the fluid. max_distance : float The maximum wall distance in the flow field. rho : float, Sympy Symbol/Expr, str The density. If `rho` is a str then it is converted to Sympy Function of form 'rho(x,y,z,t)'. If 'rho' is a Sympy Symbol or Expression then this is substituted into the equation. Default is 1. dim : int Dimension of the Zero Equation Turbulence model (2 or 3). Default is 3. time : bool If time-dependent equations or not. Default is True. Example ======== >>> zeroEq = ZeroEquation(nu=0.1, max_distance=2.0, dim=2) >>> kEp.pprint() nu: sqrt((u__y + v__x)**2 + 2*u__x**2 + 2*v__y**2) *Min(0.18, 0.419*normal_distance)**2 + 0.1 """ name = "ZeroEquation" def __init__( self, nu, max_distance, rho=1, dim=3, time=True ): # TODO add density into model # set params self.dim = dim self.time = time # model coefficients self.max_distance = max_distance self.karman_constant = 0.419 self.max_distance_ratio = 0.09 # coordinates x, y, z = Symbol("x"), Symbol("y"), Symbol("z") # time t = Symbol("t") # make input variables input_variables = {"x": x, "y": y, "z": z, "t": t} if self.dim == 2: input_variables.pop("z") if not self.time: input_variables.pop("t") # velocity componets u = Function("u")(*input_variables) v = Function("v")(*input_variables) if self.dim == 3: w = Function("w")(*input_variables) else: w = Number(0) # density if type(rho) is str: rho = Function(rho)(*input_variables) elif type(rho) in [float, int]: rho = Number(rho) # wall distance normal_distance = Function("sdf")(*input_variables) # mixing length mixing_length = Min( self.karman_constant * normal_distance, self.max_distance_ratio * self.max_distance, ) G = ( 2 * u.diff(x) ** 2 + 2 * v.diff(y) ** 2 + 2 * w.diff(z) ** 2 + (u.diff(y) + v.diff(x)) ** 2 + (u.diff(z) + w.diff(x)) ** 2 + (v.diff(z) + w.diff(y)) ** 2 ) # set equations self.equations = {} self.equations["nu"] = nu + rho * mixing_length**2 * sqrt(G)
© Copyright 2023, NVIDIA Modulus Team. Last updated on Jan 25, 2024.