how to calculate for a range of values for different initial conditions

Question

joshua payne 2022-11-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1866813-how-to-calculate-for-a-range-of-values-for-different-initial-conditions

回答： Walter Roberson 2022-11-29

function [theta]=theta_beta_M(beta,M,gamma)
% return theta for beta-theta-M relationship for oblique shock
beta=linspace(0,(pi/2),90)
M=[1.25, 2, 6, 10)
gamma= 1.4
%cut off at Mach wave angle
if (beta<=asin(1./M)) theta=0; return; end
theta=atan(2.*cot(beta).*((M.*sin(beta)).^2-1)./(M.^2.*(gamma+cos(2.*beta))+2));

i want to be able to calculate theta values for each value of M for the range of beta.

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Answer 1

Walter Roberson 2022-11-29

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https://ww2.mathworks.cn/matlabcentral/answers/1866813-how-to-calculate-for-a-range-of-values-for-different-initial-conditions#answer_1115538

在 MATLAB Online 中打开

function [theta]=theta_beta_M(beta,M,gamma)
% return theta for beta-theta-M relationship for oblique shock
if nargin < 1; beta=linspace(0,(pi/2),90); end
if nargin < 2; M=[1.25, 2, 6, 10); end
if nargin < 3; gamma= 1.4; end
[beta,M] = ndgrid(beta, M);
theta = zeros(size(beta));
%cut off at Mach wave angle
mask = beta > asin(1./M);
theta(mask) = atan(2.*cot(beta(mask)).*((M(mask).*sin(beta(mask))).^2-1)./(M(mask).^2.*(gamma+cos(2.*beta(mask)))+2));

The result will be numel(beta) by numel(M) -- so one column for each different M value.

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Answer 2

David Hill 2022-11-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1866813-how-to-calculate-for-a-range-of-values-for-different-initial-conditions#answer_1115533

在 MATLAB Online 中打开

beta=linspace(0,(pi/2),90);
m=[1.25, 2, 6, 10];
[B,M]=meshgrid(beta,m);
gamma= 1.4;
theta=atan(2.*cot(B).*((M.*sin(B)).^2-1)./(M.^2.*(gamma+cos(2.*B))+2));
theta(B<=asin(1./M))=0
theta = 4×90
         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0         0    0.0143    0.0403    0.0644    0.0870    0.1083    0.1287    0.1483    0.1673    0.1856    0.2035    0.2210    0.2381    0.2549    0.2713    0.2875    0.3035    0.3192    0.3347    0.3500    0.3651
         0         0         0         0         0         0    0.0092    0.0349    0.0579    0.0790    0.0987    0.1175    0.1356    0.1530    0.1701    0.1867    0.2031    0.2191    0.2350    0.2506    0.2661    0.2814    0.2966    0.3116    0.3265    0.3413    0.3559    0.3705    0.3849    0.3992