Matlab required I am really dear and need your help but: Standard Solution : SIR I AM IN DEEP STRUGGLE UNDERSTAND MY SIT
Posted: Sun Jul 03, 2022 9:58 am
Matlab required
I am really dear and need your help but:
Standard Solution : SIR I AM IN DEEP STRUGGLE UNDERSTAND MY
SITUATION LIKE A BROTHER AND PLEASE GIVE ME
UPVOTE - I upvote it without getting any help, But I can not more.
Can you preferably solve task 2 for me
(task 3 is done )
thank you
1. (11 points): a. Write a program for solving the heat diffusion equation in one dimension (x-dimension) using the FTCS scheme for a delta-shaped temperature distribution (i.e., value of T=1 at x=0 and zero otherwise) as initial state (t=0) and a temperature of zero as the boundary condition at x=+-L/2. b. The correct solution is that the distribution spreads and decays in time by diffusion. Check the stability of the solution for different sets of parameters. Choose the diffusion constant equal one and choose L-1. Use N=41 sampling points on the x-axis and several values of the time step t in the range 10³ to 10%. For t=2.0x104 try several different values of N. Describe the result briefly for each condition. 0 0.5 Diffusion of a delta spike 0.02 0.00 0.05 0.045 0.04 0035 0.03 0.02 0.015 0.01 0.005 -0.5 Contour plot 0.5
2. (7 points): Show by analytical evaluation of the PDE, that the bell curve T(x,t)= with 1 [-(x-xo)² o(1)√2n 20² (1) exp o(t) = √2kt is a solution to the diffusion equation. Extract a stability rule from the temporal evolution of the standard deviation & (Hint: Calculate the duration for the increase of a from 0 to h, with h being the grid spacing). Is this consistent with the empirical result from problem 1? 3. Optional problem (+5 points): Apply von-Neumann stability analysis to the advection equation / Lax-Wendroff scheme. Calculate the absolute value of the gain factor 5 (analytical calculation). Derive the stability rule Tmax by discussing the maximum of 15 for the following cases: Hint: Identify the maxima of the terms of 15 | by varying the argument x-k-hj of the sine and cosine functions. Plot || as a function of x on the interval 0 to 2x for the three cases, respectively. Note: This problem is analytical, i.e., to be solved on paper. You may use Matlab to make the plot.
6 5 4 3 2 - 0 0.5 Diffusion of a delta spike 0 -0.5 0.02 0.04 Time 0.06
Time 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 -0.5 Contour plot 24 ++ 0 XO tur tw ta 0.5
alpha=k*dt/dx^2; L=1; t=1; k=.001; n=11; nt=500; dx=L/n; dt=.002; TO (1)=400; for j=1:nt for i=2:n T1(i)=TO (i) +alpha* (TO(i+1)-2*TO (i) +TO (i-1)); end TO=T1; end plot(x,T1) Bro iam in the deep struggle understand my situation like brother give me upvote
3) Qustan H stability Van 2 -3 of the forend Neemann analyour.. |f|≤ 1 Thux explacing the semuat of a Jenu Ach being DAI R inkad of equation at time to in terme let us M² (1.1) 1 og f= Mumsical Schchen (Grosser) compared to the exeat Rolution (subt) at time goe caith spatial good point. intend f=1- approx. the desting for the heat forward finite defiene The condith conditions. small of ² 3 st 03 f schome- At ² DOF 12 Cd ux look at the stability trop of 16 Neuman & methool. The amplification factor in this cose calific consider an appoor. 1 1+4 ++ 201² (115) uxy Alable. 3333333 C C C la na 300A An C
} 3 Consider the forword in time centered numerical h+1 in space schome for the heat equatur harmonies amplification. (w²11 - 20;" + 4) consider simple solution for the differen& equatin. on the form w.h=ph. eigh| where i = 1 thought of as where w + and I 16 an integer which can be version of the forsier descrete the the amplitude. II known if & only fuction sulfi Cose Indesting A numerical scheme for an if the AFD 4x2 a skep the details 12 |P) ≤ 1 + 0 (AH) associated evolution equation of the proof here but in the fact that in that lever hut shell is due to the lesgest er eigan value of the differenc the expression of with into the forward Dat f = 1 + ( with - stable 14 fargest amplificaten 2+2mith J=1- (1- ( 11h)
I am really dear and need your help but:
Standard Solution : SIR I AM IN DEEP STRUGGLE UNDERSTAND MY
SITUATION LIKE A BROTHER AND PLEASE GIVE ME
UPVOTE - I upvote it without getting any help, But I can not more.
Can you preferably solve task 2 for me
(task 3 is done )
thank you
1. (11 points): a. Write a program for solving the heat diffusion equation in one dimension (x-dimension) using the FTCS scheme for a delta-shaped temperature distribution (i.e., value of T=1 at x=0 and zero otherwise) as initial state (t=0) and a temperature of zero as the boundary condition at x=+-L/2. b. The correct solution is that the distribution spreads and decays in time by diffusion. Check the stability of the solution for different sets of parameters. Choose the diffusion constant equal one and choose L-1. Use N=41 sampling points on the x-axis and several values of the time step t in the range 10³ to 10%. For t=2.0x104 try several different values of N. Describe the result briefly for each condition. 0 0.5 Diffusion of a delta spike 0.02 0.00 0.05 0.045 0.04 0035 0.03 0.02 0.015 0.01 0.005 -0.5 Contour plot 0.5
2. (7 points): Show by analytical evaluation of the PDE, that the bell curve T(x,t)= with 1 [-(x-xo)² o(1)√2n 20² (1) exp o(t) = √2kt is a solution to the diffusion equation. Extract a stability rule from the temporal evolution of the standard deviation & (Hint: Calculate the duration for the increase of a from 0 to h, with h being the grid spacing). Is this consistent with the empirical result from problem 1? 3. Optional problem (+5 points): Apply von-Neumann stability analysis to the advection equation / Lax-Wendroff scheme. Calculate the absolute value of the gain factor 5 (analytical calculation). Derive the stability rule Tmax by discussing the maximum of 15 for the following cases: Hint: Identify the maxima of the terms of 15 | by varying the argument x-k-hj of the sine and cosine functions. Plot || as a function of x on the interval 0 to 2x for the three cases, respectively. Note: This problem is analytical, i.e., to be solved on paper. You may use Matlab to make the plot.
6 5 4 3 2 - 0 0.5 Diffusion of a delta spike 0 -0.5 0.02 0.04 Time 0.06
Time 0.05 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 -0.5 Contour plot 24 ++ 0 XO tur tw ta 0.5
alpha=k*dt/dx^2; L=1; t=1; k=.001; n=11; nt=500; dx=L/n; dt=.002; TO (1)=400; for j=1:nt for i=2:n T1(i)=TO (i) +alpha* (TO(i+1)-2*TO (i) +TO (i-1)); end TO=T1; end plot(x,T1) Bro iam in the deep struggle understand my situation like brother give me upvote
3) Qustan H stability Van 2 -3 of the forend Neemann analyour.. |f|≤ 1 Thux explacing the semuat of a Jenu Ach being DAI R inkad of equation at time to in terme let us M² (1.1) 1 og f= Mumsical Schchen (Grosser) compared to the exeat Rolution (subt) at time goe caith spatial good point. intend f=1- approx. the desting for the heat forward finite defiene The condith conditions. small of ² 3 st 03 f schome- At ² DOF 12 Cd ux look at the stability trop of 16 Neuman & methool. The amplification factor in this cose calific consider an appoor. 1 1+4 ++ 201² (115) uxy Alable. 3333333 C C C la na 300A An C
} 3 Consider the forword in time centered numerical h+1 in space schome for the heat equatur harmonies amplification. (w²11 - 20;" + 4) consider simple solution for the differen& equatin. on the form w.h=ph. eigh| where i = 1 thought of as where w + and I 16 an integer which can be version of the forsier descrete the the amplitude. II known if & only fuction sulfi Cose Indesting A numerical scheme for an if the AFD 4x2 a skep the details 12 |P) ≤ 1 + 0 (AH) associated evolution equation of the proof here but in the fact that in that lever hut shell is due to the lesgest er eigan value of the differenc the expression of with into the forward Dat f = 1 + ( with - stable 14 fargest amplificaten 2+2mith J=1- (1- ( 11h)