@@ -185,8 +185,7 @@ def get_flux_hlld(
185185 )
186186
187187 # Step 2
188- # Compute left & right wave speeds according to Miyoshi & Kusano, eqn. (67)
189- #
188+ # Compute left & right wave speeds according to Miyoshi & Kusano, eqn. (67)
190189
191190 pbl = 0.5 * (Bxi ** 2 + By_L ** 2 )
192191 pbr = 0.5 * (Bxi ** 2 + By_R ** 2 )
@@ -205,7 +204,6 @@ def get_flux_hlld(
205204
206205 # Step 3
207206 # Compute L/R fluxes
208- #
209207
210208 # total pressure
211209 ptl = P_L + pbl
@@ -223,14 +221,12 @@ def get_flux_hlld(
223221 FR_By = By_R * vx_R - Bxi * vy_R
224222
225223 # Step 4
226- # Return upwind flux if flow is supersonic
227- #
224+ # Return upwind flux if flow is supersonic
228225
229226 # deferred to the end
230227
231228 # Step 5
232- # Compute middle and Alfven wave speeds
233- #
229+ # Compute middle and Alfven wave speeds
234230
235231 sdl = spd1 - vx_L
236232 sdr = spd5 - vx_R
@@ -254,7 +250,6 @@ def get_flux_hlld(
254250
255251 # Step 6
256252 # Compute intermediate states
257- #
258253
259254 ptst = ptl + rho_L * sdl * (sdl - sdml )
260255
@@ -273,7 +268,7 @@ def get_flux_hlld(
273268 ULst_By = (By_L ) * isDegen + (By_L * tmp ) * (~ isDegen )
274269
275270 vbstl = (ULst_Mx * Bxi + ULst_My * ULst_By ) / ULst_d
276- # eqn (48) of M&K#
271+ # eqn (48) of M&K
277272 ULst_E = (
278273 sdl * E_L - ptl * vx_L + ptst * spd3 + Bxi * (vx_L * Bxi + vy_L * By_L - vbstl )
279274 ) / sdml
@@ -302,8 +297,8 @@ def get_flux_hlld(
302297
303298 WRst_vy = URst_My / URst_d
304299
305- # Ul** and Ur** - if Bx is zero, same as * -states
306- # if(Bxi == 0.0)
300+ # Ul** and Ur** - if Bx is zero, same as * -states
301+ # if(Bxi == 0.0)
307302 isDegen = 0.5 * Bxsq / jnp .minimum (pbl , pbr ) < (epsilon ) ** 2
308303 ULdst_d = ULst_d * isDegen
309304 ULdst_Mx = ULst_Mx * isDegen
@@ -349,8 +344,7 @@ def get_flux_hlld(
349344 URdst_E = URdst_E + (URst_E + sqrtdr * Bxsig * (vbstr - tmp )) * (~ isDegen )
350345
351346 # Step 7
352- # Compute flux
353- #
347+ # Compute flux
354348
355349 flux_Mass = FL_d * (spd1 >= 0 )
356350 flux_Momx = FL_Mx * (spd1 >= 0 )
@@ -365,15 +359,15 @@ def get_flux_hlld(
365359 flux_By += FR_By * (spd5 <= 0 )
366360
367361 # if(spd2 >= 0)
368- # return Fl * #
362+ # return Fl*
369363 flux_Mass += (FL_d + spd1 * (ULst_d - rho_L )) * ((spd1 < 0 ) & (spd2 >= 0 ))
370364 flux_Momx += (FL_Mx + spd1 * (ULst_Mx - Mx_L )) * ((spd1 < 0 ) & (spd2 >= 0 ))
371365 flux_Momy += (FL_My + spd1 * (ULst_My - My_L )) * ((spd1 < 0 ) & (spd2 >= 0 ))
372366 flux_Energy += (FL_E + spd1 * (ULst_E - E_L )) * ((spd1 < 0 ) & (spd2 >= 0 ))
373367 flux_By += (FL_By + spd1 * (ULst_By - By_L )) * ((spd1 < 0 ) & (spd2 >= 0 ))
374368
375369 # elseif(spd3 >= 0)
376- # return Fl * *
370+ # return Fl* *
377371 tmp = spd2 - spd1
378372 flux_Mass += (FL_d - spd1 * rho_L - tmp * ULst_d + spd2 * ULdst_d ) * (
379373 (spd2 < 0 ) & (spd3 >= 0 )
@@ -392,7 +386,7 @@ def get_flux_hlld(
392386 )
393387
394388 # elseif(spd4 > 0)
395- # return Fr * *
389+ # return Fr* *
396390 tmp = spd4 - spd5
397391 flux_Mass += (FR_d - spd5 * rho_R - tmp * URst_d + spd4 * URdst_d ) * (
398392 (spd3 < 0 ) & (spd4 > 0 )
@@ -411,7 +405,7 @@ def get_flux_hlld(
411405 )
412406
413407 # else
414- # return Fr *
408+ # return Fr*
415409 flux_Mass += (FR_d + spd5 * (URst_d - rho_R )) * ((spd4 <= 0 ) & (spd5 > 0 ))
416410 flux_Momx += (FR_Mx + spd5 * (URst_Mx - Mx_R )) * ((spd4 <= 0 ) & (spd5 > 0 ))
417411 flux_Momy += (FR_My + spd5 * (URst_My - My_R )) * ((spd4 <= 0 ) & (spd5 > 0 ))
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