ana1Tests.simiSolTest

Similarity solution module

This module contains functions that compute the similarity solution for a gliding avalanche on a inclined plane according to similarity solution from : Hutter, K., Siegel, M., Savage, S.B. et al. Two-dimensional spreading of a granular avalanche down an inclined plane Part I. theory. Acta Mechanica 100, 37–68 (1993). https://doi.org/10.1007/BF01176861

Functions

Ffunction	Calculate right hand side of the differential equation : dx/dt = F(x,t) F is discribed in Hutter 1993.
analyzeResults	Compare analytical and com1DFA results :Parameters: * avalancheDir (pathlib path) – path to avalanche directory * fieldsList (list) – list of fields dictionaries * timeList (list) – list of time steps * solSimi (dictionary) –
calcEarlySol	Compute the early solution for 0<t<t_1 to avoid singularity in the Runge-Kutta integration process :Parameters: * t (numpy array) – time array * earthPressureCoefficients (numpy array) – earth Pressure Coefficients * x_0 (numpy array) – initial condition * zeta (float) – slope angle * delta (float) – friction angle * eps_x (float) – scale in x dir * eps_y (float) – scale in y dir
computeEarthPressCoeff	Computes the earth pressure coefficients function of sng of f and g i.e depending on if we are in the active or passive case
computeFCoeff	Compute coefficients eq 3.2 for the function F :Parameters: * K_x (float) – Kx earth pressure coef * K_y (float) – Ky earth pressure coef * zeta (float) – slope angle * delta (float) – friction angle * eps_x (float) – scale in x dir * eps_y (float) – scale in y dir
computeH	get flow depth from f and g solutions :Parameters: * solSimi (dictionary) – similarity solution * x1 (numpy array) – x coordinate location desiered for the solution * y1 (numpy array) – y coordinate location desiered for the solution * i (int) – time index * L_x (float) – scale in x dir * L_y (float) – scale in y dir * H (float) – scale in z dir * AminusC – A-C coefficient
computeU	get flow velocity in x direction from f and g solutions :Parameters: * solSimi (dictionary) – similarity solution * x1 (numpy array) – x coordinate location desiered for the solution * y1 (numpy array) – y coordinate location desiered for the solution * i (int) – time index * L_x (float) – scale in x dir * U (float) – x velocity component scale * AminusC – A-C coefficient
computeV	get flow velocity in y direction from f and g solutions :Parameters: * solSimi (dictionary) – similarity solution * x1 (numpy array) – x coordinate location desiered for the solution * y1 (numpy array) – y coordinate location desiered for the solution * i (int) – time index * L_y (float) – scale in y dir * V (float) – y velocity component scale
computeXC	get center of mass location :Parameters: * solSimi (dictionary) – similarity solution * x1 (numpy array) – x coordinate location desiered for the solution * y1 (numpy array) – y coordinate location desiered for the solution * i (int) – time index * L_x (float) – scale in x dir * AminusC – A-C coefficient
defineEarthPressCoeff	Define earth pressure coefficients
getReleaseThickness	Define release thickness for the similarity solution test
getSimiSolParameters	get flow depth, flow velocity and center location of flow mass of similarity solution for required time step
mainSimilaritySol	Compute similarity solution :Parameters: simiSolCfg (pathlib path) – path to simiSol configuration file
odeSolver	Solve the ODE using a Runge-Kutta method :Parameters: * solver (ode instance) – ode instance corresponding to out ODE * dt (float) – time step * t_end (float) – end time * solSimi (dictionary) –
postProcessSimiSol	loop on all DFA simulations and compare then to the anlytic solution
prepareParticlesFieldscom1DFA	get fields and particles dictionaries for given time step, for com1DFA domain origin is set to 0,0 for particles - so info on domain is required